THE  LIBRARY 

OF 

THE  UNIVERSITY 
OF  CALIFORNIA 

LOS  ANGELES 

MUSIC  LIBRARY 

GIFT  OF 
GERALD  SCORDAN 


A   PRACTICAL    INTRODUCTION 
TO   COMPOSITION 


HARMONY    SIMPLIFIED 


BY 

FRANCIS    L.    YORK,    M.  A. 


REVISED    AND    ENLARGED    EDITION 


FOURTH  EDITION 


$I.OO 


BOSTON 

OLIVER   DITSON   COMPANY 

NEW  YORK  CHICAGO  PHILADELPHIA 

CHAS.  H.  DITSON  &  Co.  LYON  &  MEALY  J.  E.  DITSON  &  Co. 


Copyright,  MDCCCXCVII,  by 
F.  L.  YORK 

Copyright,  MCM,  by 
OLIVER  DITSON  COMPANY 

Copyright,  MCMI,  by 
OLIVER  DITSON  COMPANY 

Copyright,  MCMIX,  by 
OLIVER  DITSON  COMPANY 


TO  MY  FRIEND, 

FREDERIC   H.   PEASE, 

MICHIGAN  STATE  NOKMAL  COLLEGE, 

THIS  LITTLE  BOOK  IS  RESPECTFULLY 
DEDICATED. 


USTTEODTJOTOET. 


IN  the  following  pages  I  shall  endeavor  to  give,  in  the  simplest 
possible  form,  an  outline  of  the  principles  of  Harmony.  I  shall 
make  no  attempt  to  give  details  or  to  deal  with  the  subject 
exhaustively,  but  I  shall  present  all  the  tone  combinations  found 
in  music,  and  give  sufficient  explanations  of  their  use  to  enable 
the  student  to  recognize  them  in  the  works  of  others  and  use  them 
correctly  in  his  own.  The  rules  given  are  derived  entirely  from 
the  analysis  of  the  works  of  the  great  composers,  and  are 
followed  by  them  in  the  great  majority  of  cases.  It  must  be 
remembered  that  the  canons  of  art  are  not  moral  laws,  but  simply 
state  what  is  expedient  in  general.  Violations  of  the  rules  — 
which  occur  frequently  in  the  best  compositions  —  do  not  concern 
us.  Irregularities  and  exceptions  do  not  come  within  the  scope 
of  this  work.  It  will  therefore  be  necessary  to  leave  untouched 
many  interesting  and  instructive  points,  but  it  is  hoped  that  by 
omitting  all  detail  the  student  will  gain  a  clearer  insight  into  the 
essentials  of  musical  composition.  A  sufficient  knowledge  of 
piano  playing  to  enable  the  student  to  play  an  ordinary  hymn- 
tune  is  presupposed. 

This  work,  in  its  inception,  appeared  in  1895  in  serial  form  in 
one  of  the  musical  periodicals.  The  demand  for  it  was  so  great, 
that  it  became  necessary  to  gather  the  chapters  into  a  book  form,, 
and  the  great  success  of  the  latter,  together  with  the  desirability 
of  amplification  made  clear  by  its  use  in  the  hands  of  teachers, 
led  to  the  present  revised  and  enlarged  edition. 

FRANCIS  L.   YORK. 
DETROIT,  August,  1900. 


CONTENTS. 


CHAPTER  PAGE 

I.  Definition  of  Harmony,  Chord,  Triad;  Tonic  and  Dominant 
Chords;  Character  of  the  Tones  of  the  Scale  ;  Four-voiced  Com- 
position ;  Doubling  ;  Open  and  Close  Position 1 

II.  Harmony  and  Melody  ;  Voice  Progression  ;  Parallel  Fifths  and 
Octaves ;  Leading  Tone  ;  The  Sub-Dominant ;  Normal  Progres- 
sion    6 

III.  Intervals.     Normal  ;  Major,  Minor,  Augmented,  and  Diminished   .  12 

IV.  Authentic  Cadences  ;  Parallel,  Contrary,  and  Oblique  Motion ;  In- 

versions ;  Ic 18 

V.     Dissonance  ;  Resolution  ;  Preparation  ;  Dominant  Seventh  ;  Method 

of  Writing  Exercises 21 

VI.     Use  of  Chords  in  Various  Positions  (Inversions) 26 

VII.     Review 31 

VIII.     Major  and  Minor  Chords  ;  Super-Tonic 34 

IX.     Relation  of  Minor  Chords  ;  Mediant  and  Sub-Mediant 37 

X.     Half,  Imperfect,  Plagal,  and  Surprise  Cadences ;  Concealed  Fifths 

and  Octaves .  41 

XI.     The  Diminished  Triad  ;  The  b  and  c  Positions  of  Minor  Chords      .  45 

XII.     Minor  and  Diminished  Chords  with  Minor  Seventh 48 

XIII.  Major  Chords  with  Major  Seventh  ;  Chords  of  the  Ninth,  Eleventh, 

and  Thirteenth 53 

XIV.  Irregular  and  Passive  Progressions  ;  By-Tones 57 

XV.     Review 63 

XVI.     Minor  Mode ;  i,  V,  iv  and  V7    .     .     .     . 65 

XVII.     Minor  Mode  Continued.     Secondary  Chords 68 

XVIII.     Minor  Mode  Concluded.     Seventh  Chords 71 

XIX.     Transition  or  Modulation  ;  Passing,  Complete.     Bridge  Chord    .     .  76 

XX.     Use  of  Tones  Foreign  to  the  Key  ;  Altered  Chords 81 

XXI.     Chromatic  Chords  ;  Distinction  between  Transitional,  Altered,  and 

Chromatic  Chords 86 

XXII.     Mixed  Chords ;    The  French,  Italian,  and  German  Chords  of  the 

Sixth  ;  Forms  of  the  Diminished  Seventh 90 

XXIII.  The  Flatted  VI  and  Flatted  II;    Explanation  of  Some  Irregular 

Progressions 94 

XXIV.  Non-Harmonic  Tones  ;  Passing,  Changing,  Appoggiaturas      ...  97 
XXV.     Anticipatory  Tones  ;  Pedal  Point 100 

XXVI.     Suspensions  or  Retardations.     Conclusion 104 

XXVII      Figured  or  Thorough  Bass 109 

APPENDIX  A.     Characteristic  Effect  of  Each  Tone 114 

APPENDIX  B.     Additional  Exercises 117 


HARMONY  SIMPLIFIED. 


CHAPTER   I. 
Definitions.     The  Tonic  and  Dominant  Chords. 

Harmony  is  the  science  of  tone  combinations  and  the  art  of 
using  such  combinations. 

A  chord  is  a  combination  of  tones  that  gives  the  hearer 
an  impression  of  unity  and  completeness.  It  is  not  necessary 
that  the  tones  of  a  chord  be  sounded  together ;  they  may  appear 
successively,  as  the  sixteenth  notes  in  Figure  1,  a,  forming  what 
is  known  as  a  broken  chord.  The  combinations  given  in 
Figure  1,  b  and  c,  are  not  chords.  Chords  are  formed  by  build- 
ing up  thirds;  as  C,  E,  G,  or  G,  B,  D,  F,  Figure  1,  d,  e. 
Chords  of  three  (different)  tones  are  called  triads. 


•  Chords  are  numbered  by  the  Roman  numerals  correspond- 
ing to  the  degree  of  the  scale  on  which  they  are  based :  thus  the 
chord  on  the  first  degree  of  the  scale,  Doh,  Me,  Soh,  is  num- 


2  HARMONY  SIMPLIFIED. 

bered  I ;  on  the  fifth  of  the  scale,  Soh,  Te,  Ray,  is  numbered  V. 
The  I  is  called  the  tonic  chord;  the  V  is  called  the  domi- 
nant chord. 

Each  chord  has  a  character  of  its  own  which  is  derived  largely 
from  the  character  of  the  tone  on  which  it  is  based  (the  root), 
and  partly  from  the  character  of  its  other  tones  (the  third  and 
the  fifth  above  the  root).  The  character  of  each  tone  is  as  fol- 
lows :  Doh,  firm,  tone  of  rest,  home  tone.  Ray,  aspiring,  ex- 
pectant. Me,  plaintive,  quiet.  Fah,  solemn,  desolate.  Soh, 
bold,  bright.  Lah,  sorrowful.  Te,  piercing,  pressing  upward.* 

The  most  important  chords  are  the  I  and  the  V.  The  I 
(formed  on  Doh)  is  the  chord  toward  which  all  the  chords  tend, 
and  in  which  they  all  finally  come  to  rest.  The  V  (formed  on 
Soh)  dominates  the  key;  it  demands  that  the  I  follow  imme- 
diately. 

In  the  case  of  each  chord  notice  the  effect  of  the  component 
tones.  The  I,  composed  of  Doh,  Me,  and  Soh,  is  the  chord  of 
rest  (Doh),  of  quiet  (Me),  and  yet  it  is  a  bright  chord  (Soh). 
The  V,  composed  of  Soh,  Te,  and  Ray  is  bold  (Soh),  expectant 
(Ray),  and  restless  (Te)  ;  the  effect  of  the  chord  depends  some- 
what on  the  tone  in  the  highest  part.  See  Figure  2,  a,  b. 

Each  chord,  except  the  I,  has  a  more  or  less  strong 
tendency  to  move  to  some  special  one  of  the  other 
chords  —  usually  to  that  chord  whose  root  is  five  tones 
lower.  As  the  V  to  the  I,  Figure  2,  c. 


Root.  Root. 
V    V    V      V      I      I 


*  For  illustrations  of  the  use  that  composers  make  of  these  characteris- 
tics, see  Appendix,  p.  109. 


HARMONY  SIMPLIFIED.  3 

As  composition  is  based  on  four-voiced  (four-part)  writing, 
our  exercises  will  all  be  written  as  if  for  four  singers,  soprano, 
alto,  tenor,  and  bass.  As  most  chords  contain  but  three  (dif- 
ferent) tones,  one  tone  of  the  chord  must  appear  in  two  voices  at 
once  ;  that  is,  that  tone  is  doubled. 

Rule  1.  —  In  doubling,  the  best  tone  is  the  root,  the  next  best 
is  the  fifth,  and  the  poorest  is  the  third.  *  Figure  3,  a.  In  the 
first  chord  the  soprano  and  the  bass  each  have  C,  thus  doubling 
the  root.  The  third  chord  has  the  fifth,  G,  doubled  by  the  tenor 
and  the  soprano.  The  last  six  chords  all  contain  the  doubled 
third,  and  the  effect  is  much  less  pleasant.  See  also  Figure  46,  a. 


3. 


Good.      Good.    Less  good        ??  ??  ??  Bad.       Bad.        Bad. 

,    but  correct.  "$"? 


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1.1 

When  the  three  upper  voices,  soprano,  alto,  and  tenor,  are 
within  an  octave,  the  harmony  is  said  to  be  close,  or  the  chords 
are  said  to  be  in  close  position.  All  the  chords  in  Figure  3,  b, 
are  in  close  position.  When  there  is  a  tone  of  the  chord  omitted 
from  between  two  of  the  upper  parts,  the  chord  is  said  to  be  in 
open  position.  In  Figure  3,  a,  the  first  chord  is  in  open  posi- 
tion, because  a  G  might  have  been  placed  between  the  soprano 
and  the  alto,  bringing  the  three  tones  within  an  octave.  All  the 
chords  in  Figure  3,  a,  except  one  (which?)  are  in  open  position. 


*  Still  the  third  may  be  doubled,  if  by  so  doing  a  decidedly  better  leading 
of  the  parts  is  secured. 


HARMONY  SIMPLIFIED. 


See  also  Figure  13,  page  10,  in  which  most  of  the  chords  are  in 
close  position. 

For  the  pi%esent  all  exercises  are  to  be  written  in  the  key  of  C. 


Exercise. 

First.  —  Write  I  and  V  chords  in  various  forms,  doubling  the 
tones  according  to  Rule  1,  and  using  the  close  position. 

Second.  —  Write  as  before,  using  only  the  open  position. 
The  bass  must  in  all  cases  have  the  root,  and  every  chord  should 
have  underneath  it  its  proper  numeral. 

Third. —  Have  some  friend  play  the  chords  in  the  exercises 
thus  written,  and,  without  looking,  name  each  chord  as  it  is 
played. 

In  the  following  chant  by  Tallis  (transposed)  all  the  chords 
but  one  are  I  or  V. 

T.  TALLIS. 


4. 


_t7    fa    "fig _|_ |^_ 


1 


I          I    •      V         I  IV  VVI 

The  following  (transposed)  from  Mendelssohn's  "Song  with- 
out Words,"  No.  41,  is  made  entirely  of  these  two  chords. 

MENDELSSOHN. 


f  f  '* 


d 'f-*-i 

i= 

fTm  • ' •  • ' 


HARMONY  SIMPLIFIED. 
Mark  the  I  and  V  chords  in  the  following. 


KUHLAU. 


6. 


m 


b. 

-f- 


m 


CLEMENTI. 
-t-t- 


^ 


HARMONY  SIMPLIFIED. 


CHAPTER    II. 

Movement  of  Voices.     The  Sub-Dominant  Chord. 
Normal  Progression. 

In  writing  music  there  are  two  most  important  things  to  con- 
sider. First,  the  progression  or  movement  of  each  chord  as 
a  whole,  and,  second,  the  movement  of  each  tone  in  the  chord. 
In  other  words,  we  must  examine  our  work  perpendicularly  for 
harmony,  and  horizontally  for  melody. 

Rule  2.— When  two  different  chords  (as  I  and  V)  follow  one 
another  directly  and  contain  a  tone  that  is  common  to  each  (as 
Soh  in  the  V  and  I),  this  common  tone  should  remain  in  the  same 
voice  or  part.  Figure  7,  a  and  b. 

Rule  3.— Bach  tone  should  progress  to  the  nearest  tone  pos- 
sible. Figure  7,  a  and  b. 


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Good.               Good.               Bad. 

Good.                 ?             Good. 

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7. 


Observance  of  these  two  rules  gives  smoothness  to  a  composi- 
tion and  avoids  the  jerky  effect  produced  by  voices  skipping 
about. 

Rule  4.— Two  voices  should  not  make  the  same  progression 
•when  they  are  either  a  fifth  or  an  octave  apart.  Such  a  progres- 
sion is  called  parallel  fifths  or  octaves.*  Figure  8,  a. 


*  Parallel  octaves  do  not  seriously  offend  the  ear,  but  if  two  voices  move  in 
octaves  the  result  is  that  we  really  drop  out  one  voice  and  are  writing  in  three 
parts,  since  one  part  loses  its  independence  and  simply  doubles  another  part  at 


HARMONY  SIMPLIFIED.  7 

Rule  5.— The  seventh  of  the  scale,  Te  (also  called  the  lead- 
ing tone),  must  move  upward  to  the  eighth,  Doh,  if  the  follow- 
ing chord  contains  Doh.  Figure  8,  b.  It  is  the  character  of  Te 
to  demand  Doh  as  the  following  tone,  and  this  demand  should  be 
satisfied,  no  matter  in  which  voice  Te  may  be.* 


8. 


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l__ gilt     gy          ^        hg— 

£-» — 1   /        __    *rr ^J2~S!!± 


In  distributing  the  tones  of  a  chord  among  the  four  voices, 
keep  the  voices  as  nearly  equidistant  as  possible.  No  two  adja- 
cent parts  (except  the  tenor  and  bass)  should  be  over  an  octave 
apart.  The  first  two  chords,  Figure  9,  a,  are  well  arranged,  the 
next  two  are  badly  distributed.  The  tenor  and  bass  may  be  any 
reasonable  distance  apart,  Figure  9,  a,  the  fifth  chord. 

The  root  may  be  trebled,  that  is,  may  appear  in  three 
parts  at  once  (as  at  Figure  9,  5),  the  fifth  being  then  omitted.  The 
third  must  not  be  omitted.  Figure  9,  b.  The  third  must  be 
present  or  the  chord  lacks  the  necessary  element  of  completeness  J 
see  definition  of  chord,  also  Figure  1,  b. 


the  distance  of  an  octave.  Parallel  fifths  sound  very  badly.  Let  the  student 
play  the  following  well-known  melody  with  the  second  voice  a  fifth  lower,  as  writ- 
ten, and  he  will  not  care  to  introduce  such  effects  into  his  compositions. 


*  Te  is  not  infrequently  found  moving  down  to  Soh,  when  it  is  in  an  inner 
voice  and  the  bass  moves  in  contrary  motion. 


HARMONY  SIMPLIFIED. 


9. 


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J\            /"2 

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The  chord  next  in  importance  is  the  IV,  called  the  sub- 
dominant  (i.  e.,  under-dominant),  formed  on  Fah  the  fifth  be- 
low Doh,  just  as  the  dominant  is  formed  on  Soh.  the  fifth  above 
Doh.  The  IV  contains  no  tone  found  in  the  V,  hence  it  con- 
trasts strongly  with  it.  Its  character  is  solemn  (Fah),  restful 
(Doh),  and  inclined  to  sadness  (Lah).  Compare  the  "Amen 
Close  "  in  church  music.  Figure  10. 


10. 


y 

1                     1 

H 

2t 

1                                            \        S3               S3 

EtS 

\        0               « 

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A    - 

men.          A    -  men.          A    -  men. 

pv  •          gj 

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1                         1 

1                         1 

The  three  chords,  I,  V,  IV,  contain  all  the  tones  of  the  scale ; 
two  of  the  tones,  Doh  and  Soh,  appearing  in  two  chords,  as  shown 
in  the  following. 


IV 


Fah     Lah     Doh     Me     Soh     Te     Ray  iv       I        v 

FA         C        E       G        B       D-in  the  key  of  C. 


We  have  said  that  a  chord  usually  progresses  to  a  chord 
whose  root  is  a  perfect  fifth  below.  This  is  called  the  normal 
progression.  The  IV  cannot  make  this  progression,  as  the  per- 


HARMONY  SIMPLIFIED. 


feet  fifth  below  its  root  does  not  lie  in  the  key — as  we  shall  learn 
in  the  next  chapter.  But  as  all  chords  have  a  tendency  towards 
the  I,  the  IV  goes  to  the  I  either  directly  or  first  to  the  V,  and 
then  to  the  I. 

Rule  6.— The  V  must  not  go  to  the  IV.     Try  it  and  see  how 
badly  it  sounds. 


11. 


The  student  should  play  the  chords  in  Figure  11,  noticing  the 
effect  of  the  I,  V,  and  IV  chords.  He  should  then  at  the  piano 
discover  for  himself  other  distributions  of  these  chords,  naming 
them  as  he  plays.  Figure  12  shows  the  use  of  these  chords. 

HANDEL.     "Samson." 


VL_^  (2.  —  L-O.  <2.  —  U—^  .__ 

~^  •    & 

Good.                Good. 

Good. 

Bad. 

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11 

IV     IV       IV        I        IV         I 

IV        V         I 

V 

IV 

V       I 


^ 


* 


II 


IV 


The  following  from  Chopin's  eleventh  "Nocturne"  shows  what 
can  be  done  by  a  master  with  the  small  material  that  we  have  al- 
ready studied. 


10 


HARMONY  SIMPLIFIED. 


13. 


F.  CHOPIN,  op.  37,  No.  1. 


• 


Let  the  student  first  name  these  chords  from  the  paper.  Af- 
terward the  teacher  should  play  them  at  the  piano  and  ask  the 
student  to  name  as  many  of  the  chords  as  he  can  by  the  sound,— 
he  should  know  all  the  chords  but  the  two  marked  with  a  cross. 


Exercise. 

First.— Write  two  or  more  exercises  in  the  key  of  C  using  the 
f ollowing  chords,  observing  all  the  rules  thus  far  given  :  I,  V,  V, 
I,  V,  V,  I,  I,  IV,  I,  IV,  V.  I.  Write  in  common  time,  aU  half  notes 
but  the  last  which  is  a  whole  note.  Figure  14  shows  some  things 
to  be  imitated  and  some  things  to  be  avoided.  From  a  to  b  no 
error.  At  b  parallel  octaves.  At  c  the  third  is  omitted :  c  to  d 
parallel  fifths  (between  alto  and  bass).  At  f  Te  does  not  go  to 
Doh. 


Tg=^~g— *=&— =j- 

<•>  I       I <&— \— -£^—<si— ^ 


IV      I      IV      V 


Second.— Let  the  student  discover  for  himself  the  errors  in 
the  following  and  write  out  the  example  in  corrected  form, 
^here  are  at  least  fifteen  violations  of  the  rules  so  far  given. 


HARMONY  SIMPLIFIED. 


11 


_n.    — 1_  ^ 


* 


&-V&—&+ 


r 


r 


Third.— Mark  the  I,  V,  and  IV  chords  in  the  ifollowing,  Fig- 
ure 16.     The  notes  in  parenthesis  do  not  belong  to  the  harmony. 


16. 


i 


/ 


e 


"  Gloria  in  Excelsis." 


I 


H= 1=:^: 

ZC 


_.L ^_ 


tp=p 

-&- 


1 


£ 


-1= 


Fourth.— The  melody  in  Figure  17  is  to  be  harmonized  with 
the  following  chords :  I,  IV,  V,  I,  I,  V,  I,  I,  IV,  V,  I. 


17. 


\\ 


12 


HARMONY  SIMPLIFIED. 


CHAPTER   III. 
Intervals. 

An  interval  is  the  difference  in  pitch  between  two  tones. 
If  the  tones  are  sounded  together  the  interval  is  harmonic  ;  if 
sounded  in  succession  the  interval  is  melodic.  Figure  18. 


Harmonic. 


18. 


^ 


Sixth.      Sixth.       Fifth.     Third.     Third.     Third.    Fourth.  Second.    Seventh. 
Melodic. 


m 


Sixth. 


Sixth.    Fifth.     Third.    Third.    Third.     Fourth.    Second.    Seventh. 


In  reckoning  intervals  count  all  the  letters  contained  in  the 
interval.  Thus  from  Doh  to  Me,  as  C  to  E,  includes  the  three 
letters,  C,  D,  E.  So  the  interval  is  a  third,  though  we  pass  over 
only  a  single  tone,  Ray  or  D.  From  C  to  A  is  six  letters  C,  D, 
E,  F,  G,  A,  hence  is  a  sixth. 

Intervals  are  always  reckoned  upward  unless  the  con- 
trary is  distinctly  stated ;  by  a  third  from  C  we  always  mean  E 
the  third  above. 

If  we  reckon  intervals  from  the  first  tone  of  a  scale,  as  C, 
they  will  all  be  major  intervals,  except  the  fourth,  fifth,  and 
octave,  which  are  usually  called  perfect.  The  intervals  formed 
on  the  scale  of  C,  then,  will  be, 


Major.        Majoi.        Perfect.       Perfect.    Major.       Major.    Perfect.    Major. 


-<9-  -&-  -&- 

Second.       Third.        Fourth.        Fifth.        Sixth.     Seventh.  Octave.    Ninth. 

When  two  tones  stand  on  the  same  degree  there  is  really  no 


HARMONY    SIMPLIFIED. 


13 


interval  formed  by  them,  but  it  is  customary  to  call  them  a  prime 
or  unison,  and  classify  them  as  forming  a  perfect  interval. 

The  intervals  are  reckoned  as  far  as  the  ninth,  although  that 
is  but  the  repetition  of  the  second  at  the  distance  of  an  octave. 
The  wider  intervals  are  usually*  reckoned  without  regard  to  the 
octave ;  thus  the  tenth  is  counted  as  a  third,  the  eleventh  as  a 
fourth,  the  twelfth  as  a  fifth.  Figure  20. 


Perfect.       Major. 


Perfect. 


Perfect. 


Major. 


=^£ 

,52  

F  —  F 

1  - 

irrv 

1  — 

1  —  .  [  

1 

1     J 

0       -^-<S>-         -<Si-                           -<S- 

-«- 

-&- 

Tenth  or                Eleventh  or         Twelfth  or           Thirteenth  or 
Tjmsonor       Third.                      Fourth.                  Fifth.                     Sixth. 

20. 


The  intervals  so  far  studied  are  all  formed  within  the  key, 
using  the  keynote  as  a  basis.  They  are,  then,  the  natural  or 
normal  intervals.  From  these,  other  kinds  of  intervals  may  be 
formed : 

First. —  If  we  increase  the  size  of  any  normal  interval  by  a 
half  step,  it  becomes  an  augmented  interval.  This  may  be 
done  in  either  of  two  ways :  by  raising  the  upper  tone  or  by  de- 
pressing the  lower  tone.  If  we  take  Figure  19,  and  sharp  the 
second  tone  or  flat  the  first  tone  in  each  measure,  the  intervals 
produced  will  be  all  augmented.  Figure  21. 


Augmented  Intervals. 


-&-  It        P-fi-  1         -<S>-   '         9-<S-  "         -i&-  P-^ 


« 

Fifths. 


Sixths.  Sevenths.  Octaves.  Ninths. 

Second.  —  If  the  major  intervals  are  made  a  half  step  smaller 
they  become  minor.  It  is  only  from  major  intervals  that  minor 
intervals  can  be  made,  never  from  perfect  intervals.  Figure  22, 


*Not  always.     See  Chapter  XIII. 


14 


HARMONY  SIMPLIFIED. 


Minor  Intervals. 


22.  : 


Third.  —  If  the  perfect  or  the  minor  intervals  are  contracted 
by  a  half  step  they  become  diminished.  In  Figure  23,  the  di- 
minished intervals  are  formed  from  the  minor  intervals  of  Figure 
22,  by  raising  the  lower  tone  or  by  lowering  the  upper  tone  a 
half  step. 

Diminished  Intervals. 


Second. 


Thirds. 


When  we  have  Oft —  Db,  although  there  is  theoretically  an 
interval  (that  is,  a  difference  in  pitch),  practically  there  is  none, 
and  the  two  letters  are  nothing  more  than  two  ways  of  writing 
the  same  pitch :  such  an  interval  is  called  enharmonic. 

The  diminished  intervals  in  Figure  24  are  all  formed  from 
perfect  intervals. 

Diminished  Intervals. 


Fourths. 


Fifths. 


Octaves. 


To  determine  -whether  an  interval  is  major,  minor,  augmented, 
or  diminished,  we  proceed  as  follows.  Consider  the  lower  note 
of  the  interval  to  be  the  key  note  of  a  scale.  If  the  upper  note 
lies  in  the  scale  of  this  key,  the  interval  is  normal,  that  is,  either 
major  or  perfect.  If  it  is  a  half  step  larger  it  is  augmented.  If  a 
half  step  smaller  than  a  major  it  is  minor.  If  a  half  step  smaller 
than  a  minor  or  a  perfect  interval,  it  is  diminished.  For  ex- 
ample, we  will  find  the  names  of  the  following  intervals. 


25. 


I 


HARMONY  SIMPLIFIED. 


15 


First  count  the  letters  contained  in  each  interval.  The  first 
contains  six  letters,  D,  E,  F,  G,  A,  B{?,  and  so  is  a  sixth  ot  some 
kind.  Those  following  in  Figure  25  are  respectively  sixth, 
fourth,  seventh,  fourth,  fourth,  and  fifth.  Now  write  out  each 
interval  in  the  key  of  the  lower  tone  (Figure  26).  This  gives  us 
the  normal  intervals  corresponding  to  the  given  intervals  of 
Figure  25. 


26. 


Key  of  E.       Key  of  F. 


Key  of  Ek.    Key  of  G.       Key  of  B. 


By  comparing,  we  find  the  first  interval  (Figure  25)  to  be  a 
half  step  less  than  the  normal  major  sixth  (Figure  26),  and 
hence  is  a  minor  sixth.  The  second  is  a  minor  sixth  for  a  similar 
reason ;  the  third  is  an  augmented  fourth,  the  fourth  a  minor 
seventh,  the  fifth  a  perfect  fourth,  the  sixth  an  augmented  fourth, 
and  the  seventh  a  diminished  fifth.  Only  one  augmented  and 
one  diminished  interval  can  be  formed  within  the  scale :  Fah  to 
Te,  an  augmented  fourth,  and  Te  to  Fah,  a  diminished  fifth. 
Figure  25,  3  and  7. 

It  is  important  to  remember  that  an  interval  is  reckoned  by 
the  letters  composing  it,  and  not  by  its  appearance  on  the  key- 
board. Thus  from  C  to  E  is  a  third,  because  E  is  the  third  tone 
in  the  scale  of  C,  even  though  we  sharp  the  C  and  flatten  the  E. 
So,  Cft  to  EJ7  is  a  diminished  third,  while  from  Cft  to  Dft  is  a 
major  second,  though  the  two  intervals  are  the  same  on  the  key- 
board. 


Exercise. 

First. —Write  out  on  every  tone  of  the  scale  of  C  all  the 
major,  minor,  perfect,  augmented,  and  diminished  intervals. 


16 


HARMONY  SIMPLIFIED. 


Second.  —  Analyse  the  following  from  Chopin  (Figure  27), 
reckoning  upward  from  the  lower  note,  and  marking  the  inter- 
vals thus :  —  the  major  with  a  capital  M,  the  minor  with  a  small 
m,  the  perfect  with  P,  the  augmented  with  A,  and  the  diminished 
with  D. 


27. 


P.  5th.    P.  4th.  A.  4th.  etc. 

Third.  —  Mark  in  the  same  way  the  following. 


28. 


:??: 


is=q=|£ 


-$*. 


\\ 


Fourth.  — "Write  the  intervals  indicated  in  the  following. 


29. 


M.  3rd.      m.  6th.  M.  6th.          A.  5th.          P.  4th.        m.  7th.          A.  3rd. 


""      f~'~  '  ^n P" ~~f~ 


^1 


ty 


D.  7th.      M.  7th.      m.  3rd.        M.  6th.      D.  5th.      m.  2nd.  M.  2nd.    D.  4th.        P.  5th. 


I 


HARMONY  SIMPLIFIED. 


17 


Fifth.  -  The  teacher  should  require  the  pupil  to  tell,  by  the 
Bound  only,  various  intervals  when  played  on  the  piano  or 
•when  sung  by  two  voices,  or  when  played  on  the  violin.  A  few 
minutes  should  be  spent  at  every  lesson  in  training  the  ear  in 
this  way,  and  the  practice  should  be  continued  throughout  at 
least  one  half  the  course.* 


Sixth.  —Add  the  alto  and  tenor  parts  (the  inner  parts)  to  the 
soprano  and  bass  given  in  the  following. 


3O. 


-c*- 

m 


*It  is  hoped  that  the  student  is  already  familiar  with  Jean  Parkman  Brown's 
excellent  little  work  called  "  Intervals,  Chords,  and  Ear-training."  If  not,  a  care- 
ful reading  of  it  and  the  practice  of  the  exercises  given  in  it  will  be  of  great 
advantage. 


18 


HARMONY  SIMPLIFIED. 


CHAPTER   IV. 
Cadences.     Motion  of  Parts.     The  a,  b,  and  c  Positions. 

A  cadence  is  a  progression  of  chords  that  gives  the  hearer 
a  more  or  less  complete  feeling  of  close.  The  most  complete 
cadence  is  the  V  to  the  I,  called  the  authentic  cadence.  It 
is  perfect  when  both  chords  have  their  roots  in  the  bass,  and  the 
highest  voice  ends  on  Doh.  Figure  31,  a.  In  any  other  case  it 
is  imperfect.  Figure  31,  b. 

a.  b. 


31. 


-&  —  35  1  <5>  — 

£j               ^3d- 

x5  —  H 

&\  &  ^  — 

•?=  Va~ 

Perfect.              Perfect.             Imperfect.         Imperfect.         Imperfect. 

£>&.    ff 

«  ^  

&          \   /-23d          ^ 

^  — 

H 

The  strength  of  a  cadence,  that  is,  whether  the  feeling  of 
close  is  strong  or  not,  depends  a  great  deal  on  its  position  in  the 
composition. 

By  parallel  motion  is  meant  the  movement  of  two  voices 
in  the  same  direction.  Contrary  motion  is  movement  in  oppo- 
site direction.  In  oblique  motion  one  voice  remains  stationary 
and  the  other  moves  either  up  or  down. 


32. 


1 


Parallel. 


Bad.     Contrary. 


Oblique. 


^       & 


1 


HARMONY  SIMPLIFIED. 


19 


Contrary  and  oblique  motion  are  better  than  parallel.  A 
large  proportion  of  the  mistakes  made  by  young  writers  comes 
from  a  too  frequent  use  of  parallel  motion.  Parallel  motion  in 
all  the  parts  at  once  is  especially  to  be  avoided. 

When  the  root  is  in  the  bass  the  chord  is  uninverted  or  in 
the  a  position,  as  Ia,  read  "tonic  a  position."  Figure  33,  a. 
The  a  below  the  line  is  usually  omitted  in  writing,  and  is  used 
only  when  it  is  necessary  to  distinguish  between  different  posi- 
tions. When  any  tone  other  than  the  root  is  in  the  bass,  the 
chord  is  said  to  be  inverted  or  in  a  new  position.  When  the 
third  of  the  chord  is  in  the  bass,  the  chord  is  in  the  b  position, 
or  the  first  inversion,  as,  Ib,  read  "  tonic  b  position."  Figure  33,  b. 
When  the  fifth  is  in  the  bass,  the  chord  is  in  the  c  position,  or 
the  second  inversion,  as  Ic,  read  "tonic  c  position."  Figure  33,  c. 


S3. 


EiEdz^iEBE^zEEazz  i_*i 


-&-  -GO-  -S>- 


I  I  IIVIVTI 

aaab  bbcc 

The  only  inverted  chord  that  we  will  use  at  present  is  the  I  . 
This  chord  is  seldom  used  except  at  the  cadence. 

Rule  7.— The  Ic  must  go  to  the  V.     Figure  34,  a. 

Rule  8. — The  Ic  must  be  used  only  on  the  accented  part  of  the 
measure,  and  the  fifth  (not  the  root)  must  be  doubled.  Figure 
34,5. 


.^                ^i                       — 

'-^ 

S2                  r*2           1  r^'        ^>*i               ^ 

& 

•fK 

r"           !^> 

I  9       CS3 

—  ~e>        II 

Good.                   Good.                Uncommon. 

~&~                  S3                                          ^ 

&           &     TOD          ^5 

tt>       (^t         fl 

1              II 

1  • 

o«                                 -SJ 

Zi 

II 

*x 

Ji\         _           1 

1    a 

1 

A                    • 

L             II 

MARK.     It  is  not  always  possible  to  observe  Rules  2  and  3.     We  will  here- 

34. 


after  regard  them  as  recommendations  rather  than  as  laws. 


20 


HARMONY  SIMPLIFIED. 

Exercise. 


First. — "Write  the  following  succession  of  chords  in  the  key 
of  C.  I,  IV,  I,  V,  I,  I,  V,  V,  I,  I,  IV,  IV,  Ic,  V,  I.  Write  in  duple 
time. 

Second.— Fill  in  the  alto  and  tenor  of  the  folio-wing. 


35. 


~y  *->     I T" 


1 


Every  exercise  when  complete  should  be  played  over  by 
some  person  not  the  writer,  and  the  latter,  without  seeing  either 
the  notes  or  the  keys,  should  name  the  chords  as  they  are  played. 


HARMONY  SIMPLIFIED. 


21 


CHAPTER   V. 
Dissonances.     The  Dominant  Seventh. 

A  dissonance  is  a  combination  of  tones  that  gives  the  hearer 
a  feeling  of  unrest  and  a  desire  that  some  other  combination  fol- 
low. In  Figure  36  the  chords  marked  +  are  dissonances.  Res- 
olution is  going  from  dissonance  to  consonance — from  unrest  to 
rest.  In  Figure  36  the  unmarked  chords  are  consonant,  the  pre- 
ceding dissonant  chords  having  resolved  into  them. 


36. 


5i 

m 

•            * 

>1             J 

2 

i 

2        *i 

jjp 

Sm 

"f"^  ; 

+ 

jx.    i     j 

2.                       F 

A  dissonance  is  prepared  when  the  dissonant  tone  is  first  heard 
as  a  consonance.  Figure  37,  £>,  the  tied  notes.  A  dissonance  is 
unprepared  when  the  dissonant  tone  appears  with  the  chord. 
When  the  dissonance  is  prepared  the  effect  is  smoother,  when 
unprepared  it  is  bolder.  Figure  37,  c.  With  most  dissonances 
either  way  may  be  used. 

The  dominant  seventh  is  the  most  common  dissonant 
chord.  It  is  formed  by  adding  another  third  above  the  dominant 
triad,  thus :  Soh,  Te,  Ray,  Fah,  or,  in  the  key  of  C :  G,  B,  D,  F. 
The  new  tone,  being  at  the  distance  of  a  seventh  from  the  root, 
gives  the  name  to  the  chord.  It  is  represented  by  V?.  Figure  37, 
a,  and  Figure  36,  the  first  and  eighth  chords.  In  the  celebrated 
"  Hunting  Chorus  "  from  Von  Weber's  "  Der  Freischiitz  "  there 
are  twenty-four  measures  made  entirely  of  I  and  V7  chords.  Fig- 
ure 38. 


22 


HARMONY  SIMPLIFIED. 


37. 


Hunting  Chorus.     "Der  Freischiitz." 


( 


38.  <J 


( 


§=j — -rBJE   ^1^-J=4=^~r^=^ 
^__a — ^-^g    •  yg^p    i  — r=tp— r   i     E 


^     t:|:^    ^    A    f:   f-    f: 

£=£  EdE=|c=Jt-_jMI_tL 


Rule  9.— The  V7  must  progress  to  the  I,  Te  going  to  Doh  and 
Fah  to  Me.     Figure  37,  b  and  c. 

Te  is  sometimes  though  rarely  omitted  in  the  Vr 
On  account  of  its  strong  tendency  to  the  I,  the  V7  usually  oc- 
curs at  the  cadence.  The  restless  effect  of  this  chord  is  produced 
by  the  contradictory  character  of  the  tones  composing  it.  We 
have  added  the  solemn  and  depressing  Fah  to  a  chord  that  is 
bright,  bold,  and  aspiring.  The  conflict  of  these  two  characters 
makes  the  hearer  restless  until  the  sharp  upward-thrusting  Te 
comes  to  rest  in  the  peaceful  Doh,  and  the  desolate  Fah  changes 
to  the  quiet  Me.  If  the  student  is  inclined  to  consider  this  fanci- 
ful, let  him  play  this  V7  chord  on  the  piano  a  few  times,  leaving 
it  unresolved,  and  he  will  at  once  see  how  unsatisfying  the  effect 
is. 


Exercise. 

First.— Write  the  following  chord  succession.    I,  I,  |  V,  V,  I 
I,  I,  |  V,    I  I,   I,  I  IV,   IV,  |  Ic,   V7.  I  I  !l.     The  perpendicular  lines 
show  the  measures.     Write  in  duple  time.     Notice  that  here  the  I 
goes  to  the  V?.     This  is  even  more  common  than  the  progression 


HARMONY  SIMPLIFIED. 


23 


to  the  V  without  the  seventh,  and  is  a  stronger  progression.  It 
also  makes  a  smoother  progression  for  the  voices,  as  they  can 
move  more  by  degrees.  Figure  39. 


39. 


The  following  from  the  end  of  Schubert's  "  Impromptu,"  op.  90, 
No.  1,  is  made  entirely  of  this  progression.  Notice  how  carefully 
he  has  doubled  the  fifth  of  the  Ic,  and  led  Te  and  Fah  properly 
in  the  V?.  Although  he  has  used  more  than  four  voices,  at  the 
third  chord  from  the  end  he  has  omitted  the  G  purposely  that  we 
may  be  sure  that  the  F  has  gone  to  E. 


4O. 


The  following  is  the  method  of  writing  exercises  that  the  stu- 
dent is  advised  to  use. 

First.— Write  the  given  numerals  under  the  lower  staff. 

Second.— Write  the  bass  notes  indicated  by  the  numerals, 
choosing  such  positions  as  will  give  the  best  melody.  See  Fig- 
ure 41,  bass. 


24 


HARMONY  SIMPLIFIED. 


Third.— "Write  in  the  soprano  a  note  for  each  bass  note,  choos- 
ing tones  belonging  to  the  chord  indicated,  making  the  melody 
as  pleasing  as  possible,  using  contrary  motion  to  the  bass  more 
than  parallel  motion. 

Fourth.— Add  alto  and  tenor,  observing  the  rules  for  doub- 
ling, progression  of  chords  and  of  voices,  and  the  distribution  of 
voices. 

Fifth. — The  compass  of  the  parts  or  voices  should  be  about 
as  f ollows :  Soprano,  an  octave  and  a  half  upwards  from  mid- 
dle C.  Bass,  an  octave  and  a  half  downwards  from  middle  C. 
Alto,  a  fourth  lower  than  the  soprano.  Tenor,  a  fourth  higher 
than  the  bass. 

Sixth. — Turn  the  stems  of  the  notes  as  in  Figure  41. 

Seventh.— Figure  41  may  be  used  as  a  model.  The  student 
should  also  copy  the  bass  and  the  soprano  here  given,  add  his 
own  tenor  and  alto,  and  when  done  compare  his  work  with  the 
model. 


Exercise. 

Second.— Harmonize  the  melody  given  in  Figure  42,  using 
the  chords  indicated. 


42. 


HARMONY  SIMPLIFIED. 


25 


Third.— Acid  whatever  is  lacking  in  Figure  43.    In  measures 
six  and  seven  notice  how  the  stems  of  the  notes  are  turned. 


43. 


2  !    1 ^F       I         — Hf 


•5- 


^t 


-r 

j. 


i 


£3 


V     V      I 


The  following  from  Mendelssohn's  "  Song  without  Words,"  No. 
28,  shows  I,  Ic,  and  V7  chords  both  in  chord  form  and  as  broken 
chords. 


44. 


II  II 


V,        I 


26 


HARMONY  SIMPLIFIED. 


CHAPTER   VI. 

The  b  Position  or  First  Inversion. 
The  c  and  d  Positions. 

Each  of  the  chords  so  far  studied  may  now  be  used  with  the 
third  of  the  chord  instead  of  the  root,  in  the  bass  (b  position 
or  first  inversion),  but  all  previous  rules  must  be  followed. 
For  example,  V,  gives  us  Te  in  the  bass,  and  Te  must  go  to  Doh, 
the  same  as  if  it  were  in  an  upper  voice.  Figure  45. 


45. 


1:1 


l^SS." 


*b  Jb  LVb  LVb  vb  vb 

Rule  1O.  —  "When  a  chord  is  in  the  b  position,  do  not  double 
the  third. 

The  third  is  the  least  desirable  tone  to  double,  and  when  the 
bass  gives  it  prominence  it  must  be  omitted  in  the  other  parts. 
See  Figure  46,  a,  in  which  all  the  chords  are  either  bad  or  very 
doubtful.  The  use  of  the  b  position  gives  much  greater  free- 
dom to  the  bass,  as  we  may  now  use  any  tone  of  the  scale,  except 
Ray,  in  the  bass.  Figure  46,  6,  exhibits  chords  on  each  tone  of 
the  scale  except  Ray,  but  of  course  is  not  to  be  regarded  as  a 
harmonization  of  a  scale  progression  in  the  bass. 

a.  b. 


46. 


737"       "<5             f3     s~-      i     ^      es      \  t 

•                             I  * 

•s        f3     ^s     &     p      „      & 

f(T\   ^     -2    o           ZIZSZIS             I 

^            &       &       =>       ^        &        &     || 

J          «?  ^.        zy-< 

9-         -&-      ~       ~                 -*-     -%- 

^-^  .                              ^.          -*' 

^          S3          &            &                         II 

*~i.   2ZH3I3.                                       1 

n      S3      a 

j                  &     ^     \  ' 

^  1| 

IV     V 


HARMONY  SIMPLIFIED. 


27 


Any  triad  in  the  c  position  (second  inversion),  especially 
when  entering  on  the  accented  beat  of  a  measure,  strives  to  assert 
itself  as  a  I  .  That  is,  any  triad  in  the  c  position  sounds  like 
a  new  tonic  in  that  position,  and  requires  a  new  dominant  to 
follow,  thus  going  into  another  key.  If  the  student  will  play 
over  Figure  47,  a  and  b,  at  the  second  chord  in  each  example  he 
will  feel  the  demand  for  the  chord  that  carries  us  into  the  new 
kev. 


47. 


Q^>— ? — r  & — gg==F~ 


We  will  avoid,  then,  the  use  of  the  V    and  the  IV  ,  for  one 

C  C 

would  tend  to  carry  us  into  the  key  of  the  dominant  and  the 
other  into  the  key  of  the  sub-dominant. 

It  is,  however,  possible  to  use  these  chords  and  still  remain  in 
the  original  key.  In  order  to  do  this  we  must  take  the  following 
precautions.  We  may  use  the  Vc  if  it  is  put  on  the  un- 
accented part  of  the  measure,  when  the  bass  has  the  pro- 
gression Doh,  Ray,  Me,  or  Me,  Ray,  Doh  —  that  is,  moves 
by  degrees.  This  use  of  the  chord  though  correct  is  at  best  a 
makeshift,  and  is  only  to  be  used  in  an  unimportant  place. 
Figure  48,  a. 

The  IVC  may  be  used  with  very  good  effect  if  we  take  care 
to  put  it  on  the  unaccented  part  of  the  measure  between 
two  I  chords.  If  this  is  done  the  bass  is  of  course  stationary. 
Figure  48,  6. 


28 


HARMONY  SIMPLIFIED. 

b. 


48. 


lid — J    pg_i 


a=J  -3=3-  -^zr  I—  -  Ff- 


-<9- 


IV 


IV 


Figure    49,  the    beginning   of   a  well-known    hyinn-tune    by 
Portogallo,  illustrates  this. 


M.  PORTOGALLO. 


49. 


IV. 


IV, 


The  Chopin  study  known  as  the  "  Black  Key  Etude  "  begins 
with  I,  IV  ,  I,  repeated.  Figure  50.  As  this  is  written  in  the 
key  of  G  flat  the  1  is  G  flat,  and  the  IV  is  C  flat.  In  the  second 
measure  the  G  flat  is  held  through  by  the  pedal,  and  so  is  the 
real  bass. 


b±d 


p     •  • —  f  -i—    ^  -p-       m     _    m         m 

-^-t-^L4-4-^g=H-P  [  ^  i  &~r\\ 
i^^gFt™11'    •    I   g^l^gihl 

3 

/*      *      ^  ".      t 


HARMONY  SIMPLIFIED. 


29 


The  V7c  may  be  used  freely,  care  being  taken  that  each 
voice  progresses  properly.  The  V?b  (the  third  in  the  bass)  may 
also  be  used,  as  well  as  the  V  (the  seventh  in  the  bass).  Fig- 
ure 51.  The  V  must  go  to  the  I  and  the  V  must  go  to  the 
Ib.  Why? 


51. 


Figure  52,  part  of  the  hymn-tune,  "  St.  Thomas  ",  illustrates 
some  of  these  chords.  Let  the  student  mark  them  with  the  nu- 
merals and  also  name  them  when  played. 

"St.  Thomas.  " 


52. 


A-MEN. 


The  following  from  Beethoven  ("  Sonata  Appassionata  ")  is 
composed  entirely  of  I  and  V?  chords  in  various  positions;  being 
written  in  D  flat,  the  I  is  D  flat,  and  the  V  is  A  flat. 


53. 


7.1 


7c     v  7d 


HARMONY  SIMPLIFIED. 


cfcf-fr-tr— H — *— *r=  =*=Ft     — •J£-^:   C    l-jj-f  ^     ^^^^H 

— —  _ji.  zg: 


*•    ^:        * 


V 


7d 


7c 


The  student  should  have  this  played  to  him  and  name  the 
chords  as  they  are  played,  by  the  sound  only. 


Exercise. 

First.  —  Supply  the  parts  that  are  -wanting  in  the  following- 


54. 


-4-4, 


-U— 


I f   \  75 


Second.  —  Harmonize  the  melody  given  in  Figure  55.  The 
following  chords  are  suggested,  but  the  student  should  har- 
monize the  melody  in  several  ways,  using  different  chords 
where  practicable. 

I,  V,,  |  I,  Ib,  I  IV,  Ib,  |  V,  |  I,  V7,  |  I,  IVC,  I,  Ib,  I  Ic,  V7,  |  I  II 


65. 


Third.  —  Harmonize  the  following  bass. 


56.  l~ 


7c 


HARMONY  SIMPLIFIED. 


31 


CHAPTER   VII. 
Review. 

We  have  now  sufficient  musical  material  to  harmonize  any 
tone  of  the  scale  in  any  one  of  the  parts,  and  in  many  cases  we 
have  a  choice  of  several  chords.  Below  are  given  all  the  tones  of 
the  scale  of  C,  together  with  all  the  possible  harmonizations  so  far 
studied.  The  student  should  make  such  a  table  for  himself  and 
keep  it  for  reference,  adding  to  it  as  new  material  is  studied.  In 
this  way  he  can  tell  at  a  glance  what  harmonies  are  possible  for 
any  given  tone.  Of  course,  not  all  the  harmonies  given  as  possi- 
ble are  equally  desirable.  Usually  but  one  chord  will  be 
found  suitable  for  any  given  place.  When  there  is  a  choice, 
the  proper  chord  will  be  determined  by  the  chord  before  and  af- 
ter, by  the  position  in  the  measure,  and  by  the  progression  and 
distribution  of  the  voices. 

When  the  note  to  be  harmonized  is  in  the  soprano  we  may 
use : — 


57. 


r-y- 

1 

SZ> 

Z 

185 

b- 

gy 

-  —  & 

v2 

I 

O 

!a 

,  b  or  c 

V                   T                 TV 

a,  b  or  c       a  or  c             a, 

t)  or  c      a, 

b  or  c    I  Va  or  c 

a  or  c 

IV 

a,  b  or  c 

V                                      V 

7a,  b,  c  or  d                     7a, 

v 

b  or  c     a, 

b  or  c 

7a,  cord 

7a,  b,  c  or  d 

When  the  note  to  be  harmonized  is  in  the  bass  we  may  use  : — 


58. 


TV                   V                                           V                     V                                            V 
1Vc                V7c                                  V7d                                                         V7b 

I                  V                 I               IV                I                 IV               V 

f-^  * 

^2 

^2 

'-^ 

!• 

j-^ 

*2 

2! 

By  this  it  is  seen  that  we  have  much  greater  freedom  when 
the  soprano  is  given  than  when  the  bass  is  given. 


32 


HARMONY  SIMPLIFIED. 


It  cannot  be  too  strongly  impressed  on  the  student  that  these 
three  chords  in  their  various  positions  are  the  framework  of  all 
composition.  For  this  reason  they  are  known  as  the  primary 
triads.  Other  chords  which  we  shall  next  proceed  to  study 
(secondary  triads)  are  more  or  less  exceptional  in  their  use : 
the  I,  V,  IV,  and  V7,  constitute  nine-tenths  of  the  chords 
in  common  use. 

So  far  all  our  exercises  have  been  in  the  key  of  C.  When  we 
write  in  any  other  key  we  shall  find  the  chords  of  the  key  of  C 
having  other  names  and  characters.  Thus  C,  E,  G,  the  I  of  C 
becomes  the  IV  of  the  key  of  G,  and  the  V  of  the  key  of  F. 


IV 


I 


Key  of  C: 
Key  of  G: 
Key  of  F: 


F      A      C      E      G      B      D 


C      E      G      B      D      Fff    A 


A      C      E      G 


Exercise. 

First.— Return  to  Chapter  II.  and  write  one  exercise  from  each 
chapter  to  the  present  in  the  keys  of  G,  F,  and  A,  and  then  har- 
monize with  the  chords  given.  Figure  17  becomes : — 


InG. 


InF. 


etc. 


59.  < 


etc. 


I  IV  V  etc. 


I  IV    V  etc. 


U  I 


I  IV  V  etc. 


HARMONY  SIMPLIFIED. 


33 


In  Chapter  III.  write  the  various  intervals  in  these  three  keys. 
In  Chapter  IV.  write  Figure  35  in  these  three  keys  and  fill  in  the 
parts.  Do  the  same  with  Figure  43  in  Chapter  V.,  and  with  Fig- 
ure 54  and  55  in  Chapter  VI. 

Second.— Also  harmonize  the  following  : 


a.    Soprano  given. 


60. 


b.    Bass  given. 


±feE      ^ 


=1 

1:1 


In  the  first  fourteen  measures  of  Paderewski's  "  Minuet  a  1' An- 
tique "  there  are  no  chords  that  we  have  not  already  studied. 
Let  the  student  analyze  these  measures,  noticing  how  far  our 
rules  have  been  followed.  Figure  61. 

'  &* 

1 *-*f*- 

_  _^j *    ^ 


34  HARMONY  SIMPLIFIED. 

CHAPTER   VIII. 
Minor  Chords.     The  Super-Tonic. 

All  the  chords  so  far  studied  are  composed  of  a  major  third 
plus  a  minor  third,  and  are  called  major  chords.  Now  if  the 
first  third  is  minor,  and  the  chord  is  composed  of  a  minor  third 
plus  a  major  third,  the  chord  is  called  a  minor  chord,  as  D,  F, 
A,  or  A,  C,  E.  Minor  chords  are  represented  by  the  small 
Roman  numerals,  as  n,  m,  vi.  Figure  62.  When  we  hear  a 
minor  chord,  a  doubt  arises  as  to  which  tone  we  should  regard  as 
the  root,  the  first  or  the  third ;  for  this  reason  the  third  in  minor 
chords  is  frequently  doubled  instead  of  the  root  —  even  in  the  b 
position.  Figure  63,  a,  the  third  and  ninth  chords. 

M3d  +  m3d        M  3d  +  m  3d        m3d  +  M3d      m  3d  +  M  3d     m3d  +  M3d 

P=£: 
62. 


IV  V  n  vi 

Major  Chords.  Minor  Chords. 

The  most  common  minor  chord  is  the  one  formed  on  Ray ;  it 
is  represented  by  n,  and  is  called  the  super-tonic,  since  it  is  the 
chord  just  above  the  tonic.  The  character  of  the  chord,  as  is 
shown  by  the  tones  of  which  it  is  composed,  is  expectant  (Ray), 
solemn  (Fah),  and  somewhat  sorrowful  (Lah).  The  n  is  used 
more  often  in  the  b  position  than  with  the  root  in  the  bass. 

Rule  11.  — The  II  must  progress  to  the  V,  V7,  or  Ic. 

The  progression  of  the  n  is  the  normal  progression,  that  is,  to 
the  V,  but  as  the  Ic  demands  the  V  strongly,  the  ear  accepts  the 
Ic  as  being  only  a  delaying  of  the  progression  for  one  chord.  As 
the  V7  contains  Fah,  the  third  of  the  n,  the  progression  to  the  V_ 
is  smoother  than  to  the  V  alone.  Compare  the  progression  of  the 
Ic  to  the  V7.  Figure  39. 


HARMONY  SIMPLIFIED. 


35 


The  following  illustrates  the  use  of  the  n.  The  notes  in 
parentheses,  as  we  shall  learn  later,  do  not  belong  to  the  harmony 
at  all. 

"  America." 


63. 


H — i       i       |  -F= s— |   I  I      I—  \=\-\ iv=f — H 


'~\)  A       I 


*-*^£ 


UK       V 


1 


BEETHOVEN,  op.  14,  No.  2. 


^f- 


*=¥=H 


=fr 


--- 
=1 


s 

l__  f_  ^  lr__ 


r 

i 

ERT.     '•  Waltz/'  op.  9. 


/ 


II 

-»— J— 


4= 


v 


IV 


Exercise. 

First.  —  Harmonize  the  soprano  given  in  Figure  64. 
Second.  — Write  a  new  harmonization  of  the  same  melody, 
after  having  transposed  it  into  the  key  of  A. 


HARMONY  SIMPLIFIED. 


Third.  —  Take  the  bass  thus  formed  in  the  key  of  A,  -write  a 
new  soprano  to  it,  and  add  the  tenor  and  alto. 


64. 


•p 0- 


I 


I         V 


IV 


v      v     v7d  ib 


vb  v7b 


i       v    v 


Fourth.  —  Also  harmonize  the  bass  given  in  Figure  65. 

F^^-.^ 
65.  4- 


Let  the  student  constantly  be  on  the  lookout  for  the  chords 
he  has  learned,  trying  to  recognize  them  in  the  music  he  plays 
or  hears.  He  should  have  his  own  and  his  fellow  students'  exer- 
cises played  to  him,  and  name  the  chords  by  the  sound. 


HARMONY  SIMPLIFIED.  iJ7 

CHAPTER    IX. 
The  Mediant  and  Sub-Mediant  Chords. 

As  there  are  three  major  chords  in  each  key,  one  based  on 
the  key-note,  the  others  based  on  the  fifth  above  and  on  the  fifth 
below  the  key-note  (I,  V,  IV),  so  there  are  three  minor  chords 
which  stand  in  the  same  relation  to  each  other.  If  we  take  the 
sixth  degree,  Lah,  as  a  starting  point,  we  find  that  the  chord 
based  on  it  is  a  minor  chord  (Lah,  Doh,  Me),  and  the  chords  based 
on  the  fifth  above  (Me)  and  on  the  fifth  below  (Ray)  are  each 
minor  chords.  This  relation,  if  emphasized,  gives  rise  to  the 
minor  mode,  which  we  shall  treat  later. 


II 

A 

VI 

A  

Doh 

in 

A 

Ray       Fah 

Lah 

V 

Me 

Soh           1 

or  in  the  key  of 

C: 

II 

A 

VI 

A 

ni 

A 

D             F 

v 
A 

C 

V 

E 

G 

B 

As  in  the  case  of  the  three  major  chords,  these  three  chords 
contain  all  the  tones  of  the  scale,  two  tones  (A  and  E)  occurring 
in  two  chords.  Thus  we  have  now  two  possible  ways  of  harmo- 
nizing any  tone  of  the  scale,  and  three  possible  ways  of  harmo- 
nizing the  four  tones,  Doh,  Soh,  Lah,  and  Me.  This  does  not 
include  the  use  of  the  V7  or  of  any  inversion. 

The  chord  on  the  sixth  degree  is  called  the  sub-mediant — 
sub  meaning  "  below  "  and  mediant  meaning  "  half-way,"  because 
this  chord  is  half-way  between  the  roots  of  the  tonic  and  the  sub- 
dominant.  It  is  represented  by  vi.  The  character  of  the  chord  is 
that  of  sadness  (Lah),  the  plaintive  Me  intensifying  and  the  rest- 
ful Doh  taking  nothing  from  the  sorrowfulness  of  the  root  Lah. 


38  HARMONY  SIMPLIFIED. 

This  chord  is  much  used.  It  occurs  sometimes  in  place  of  the  I, 
and  sometimes  in  place  of  the  IV,  as  it  contains  two  tones  of  each 
of  these  chords  —  Doh  and  Me  of  the  I,  and  Lah  and  Doh  of  the 
IV.  Figure  66,  b.  Its  progression  is  the  normal  one,  that  is,  to 
the  n.  Figure  66,  c. 


66. 


b      *c 


The  chord  on  the  fifth  below  Lah,  the  n,  has  already  been 
spoken  of.  The  chord  on  the  fifth  above  Lah  is  called  the  medi- 
ant because  it  is  halfway  (mid-way)  between  the  I  and  the  V. 
It  is  the  least  useful  of  all  the  chords.  This  is  due  to  two 
causes :  First,  the  character  of  the  chord ;  Second,  its  remoteness 
from  the  I.  The  character  of  the  chord  should  be  quiet  or  plain- 
tive, being  based  on  Me,  but  the  restlessness  of  Te  and  the  bold- 
ness of  Soh  do  not  combine  well  with  this.  So  the  chord  has  an 
uncertain,  vacillating  character  that  causes  it  to  be  of  little  use 
where  progress  is  desired.  By  remoteness  from  the  I  is  meant 
that  if  we  follow  the  normal  progression  of  the  chords,  it  will 
take  four  progressions  to  reach  the  I.  Thus :  in,  vi,  11,  V,  I. 
The  relationship  between  the  mediant  and  the  I  is  not  readily 
grasped,  and  so  the  chord  is  not  much  used.  As  just  indicated, 
the  progression  of  this  chord  is  the  normal  one,  to  the  VI.  No- 
tice that  the  farther  we  go  from  the  I  the  weaker  the  progression 
of  the  chord ;  the  desire  of  the  in  for  the  vi,  and  of  the  vi  for  the 
ii  is  much  less  than  that  of  the  V  or  V7  for  the  I,  or  of  the  n  for 
the  V.  The  complete  chain  of  chords,  in,  vi,  n  (IC),V,  or  V  ,  I, 
gives  the  strongest  possible  progression. 

The  following  illustrates  the  use  of  the  three  chords  n,  in, 
and  vi. 


HARMONY  SIMPLIFIED.  39 

GUILMANT.     "  Second  Sonata  for  Organ." 


67. 


Figures  68  and    69  also  contain  examples  of   these  chords. 
Let  the  student  analyse  them,  marking  all  the  chords  in  each. 

Old  Chant. 


68. 


:±ZT_«,_ 
\—\l—Z> — 


i 


1 


jSL 


r 

WAGNER.     Bridal  Chorus  from  "Lohengrin." 


69. 


± 


iHs 


^§-t 


r- 


=«±=J=p|i==ti=S=Ff  =n 

=L«^=  =^E 


A  very  beautiful  use  of  the  mediant  chord  is  found  in 
Chopin's  "  Polonaise,"  op.  26,  No.  2.  Here-  it  gives  a  stopping, 
hesitating  effect — it  suggests  being  plucked  back  by  the  clothing 
just  as  one  is  about  to  take  a  forward  step.  Figure  70. 


70. 


/ 


!t£ 


40 


HARMONY  SIMPLIFIED. 

Exercise. 


First.— Harmonize  the  following  chord  progression.    "Write 
in   duple   time.      I,  Vb,  |  I,  VI,  |  nb,  V,  |  V7d,  Ib,  |  I,  IV,  |  Ib,  III,  | 
Vi,iib,    IC,V7>    V7,  |I.  II 

Figure  71  may  be  used  as  the  soprano  part. 


71. 


T-(g-g»-fg"~JTig—       —  -T^-hP-f      — -*g-Hg-'g  I  ^     -FigT 


The  b  position  of  these  minor  chords  may  be  used 
freely,  but  the  c  position  is  very  rare  and  had  best  be 
avoided. 

* 


72. 


EEE-ES3 


1:1 


•—  w~  r~ 


i    1 


Second. — Fill  in  the  parts  wanting  in  Figure  72.  The  stu- 
dent has  now  a  sufficient  knowledge  of  chords  to  analyse  any  ordi- 
nary hymn  tune.  Let  him  take  the  tunes  "  Old  Hundred  "  an<j 
"  "Webb  "  and  mark  all  the  chords  he  knows,  and  also  name  the 
chords  when  played  to  him. 


HARMONY  SIMPLIFIED. 


CHAPTER   X. 
Cadences.     Concealed  Fifths  and  Octaves. 

It  is  not  necessary  that  a  cadence  give  an  effect  of  complete 
close.  (See  Chapter  IV.)  Only  the  perfect  authentic  ca- 
dence does  this.  The  weaker  cadences  are  used  to  divide  the 
composition  into  rhythmical  parts,  usually  four  measures  in  length. 
Any  progression  of  chords  may  be  used  as  a  cadence,  but  certain 
ones  lend  themselves  more  readily  than  others  to  such  use,  and 
any  progression  used  as  a  cadence  is  very  greatly  affected  by  its 
position  in  the  rhythm. 

The  following  are  the  more  important  cadences : 

a. — V  or  V7  to  I,  called  the  authentic.  Figure  73,  a.  Also 
the  last  cadence  in  the  hymn  tune  "  Old  Hundred." 

b. — IV  to  I,  called  plagal  or  amen.  Figure  73,  b.  Notice 
the  parallel  fifths  in  the  last  two  measures  of  Figure  73,  b.  This 
is  not  to  be  imitated. 

c, —  I  to  V,  called  half  cadence  to  dominant.  Figure  74. 
Also  the  second  cadence  in  "  Old  Hundred." 

d.  —  I  to  IV,  called  half  cadence  to  sub-dominant. 
Figure  75. 

e. — V  or  V7  to  vi,  called  surprise  cadence,  or  deceptive 
cadence.  Figure  77,  a  and  b. 


HUMMEL.     "  Concerto,"  op.  89.  HELLER.     "  Study,'1  op.  47,  No.  4. 


73. 


'I,.       7 


42 


HARMONY  SIMPLIFIED. 

MENDE  LSSOHN.     ' '  Organ  Sonata  VI. ' 


74. 


75. 


J-|:4: 


=^=j=r 


SULLIVAN. 

£E^ 


f-f-f- 


i 


f— i— f-f 


i 


IV 


Half  cadences  (especially  to  the  V)  usually  occur  in  the 
middle  of  a  period  of  eight  or  more  measures  as  a  contrast  to  the 
authentic  cadence  at  the  end. 

f. — The  imperfect  authentic  cadence  (See  Chapter  IV)  is 
used  to  avoid  a  complete  close  in  positions  where  a  tonic  cadence 
is  expected.  Figure  76. 


MEXDELSSOHN.     "  Organ  Sonata  V." 


76. 


!^=p^EEE^ 


J J 


The  surprise  cadence  is  an  example  of  an  irregular  progression 
of  the  V7,  which  will  be  treated  later.  It  is  used  in  much  the 
same  way  as  the  imperfect  authentic. 


HARMONY    SIMPLIFIED. 

STAINER.     "Chorale." 


RIMBAULT. 


77. 


When  two  voices  move  in  parallel  motion  from  another  inter- 
val to  a  fifth  or  an  octave,  the  progression  is  called  concealed 
fifths  or  octaves.  (Notice  the  plural  name,  although  there  is 
but  one  fifth  or  octave.)  Such  progressions  are  not  desirable,  but 
are  unavoidable  at  times.  Avoid  them  between  outer  voices 
(soprano  and  bass) ;  when  the  voices  make  a  skip  or  otherwise 
call  attention  to  themselves ;  or  when  for  any  reason  the  progres- 
sion is  in  other  respects  not  as  good  as  is  desirable.  The  following 
progressions  are  all  bad. 


78. 


I3=g=! 


1 


1 


Exercise. 

First.  —  Add  the  parts  that  are  -wanting  to  Figure  79. 

Second.  —  Write  a  new  soprano  to  the  same  bass  and  add 
parts.  Notice  that  this  is  composed  of  two  four-measure  phrases, 
the  first  ending  with  a  half  cadence  to  the  V,  and  the  second  with 
a  very  strong  perfect  authentic  cadence. 


44 


HARMONY  SIMPLIFIED. 


fcftF^: 


*— » — *- 


^ 


^ 


^ 


rf 


:p: 


Z£^   ^__J_^J_J_ 

-*'               =        i 

^&~*  —  ~fiTr~ 

^-^-U 

V1-!/ 

II 

£J\  •       U      , 

II 

^w- 

«>  •  — 



9   M         (^ 

IJ 

*b    IV       »b 

Third.  —  Add  the  parts  that  are  wanting  to  Figure  8O.  This 
is  composed  x>f  four  four-measure  phrases  with  the  following 
cadences :  first,  an  imperfect  authentic  ;  second,  an  imperfect  half 
cadence  to  V  ;  third,  surprise  cadence ;  fourth,  perfect  authentic 
cadence. 


80. 


7e 


vi         V, 


HARMONY  SIMPLIFIED. 


CHAPTER   XL 
The  Sub-Tonic  or  Diminished  Chord. 

We  have  now  formed  triads  on  each  degree  of  the  scale 
except  the  seventh,  Te.  It  is  not  possible  to  form  within  the 
key  either  a  major  or  a  minor  chord  on  this  degree,  as  the  interval 
Te-Fah  is  composed  of  two  minor  thirds.  The  triad  formed 
here  is  a  diminished  chord.  It  is  called  the  sub-tonic  (below 
the  tonic),  and  is  lettered  vn°.  The  cypher  indicates  the  small 
or  diminished  fifth.  Although  the  chord  is  based  on  Te,  it  has 
no  true  root.  It  is  not  of  frequent  occurrence  in  modern  four- 
voiced  writing,  and  when  used  is  generally  treated  as  if  it  were  a 
V7  chord  with  the  root  omitted.  It  progresses  to  the  I.  The  b 
position  is  the  most  common,  and  the  so-called  root,  Te,  is  not  to 
be  doubled.  The  reason  that  Te  is  not  to  be  doubled  is  that  Te 
is  not  the  real  root ;  also  being  the  leading  tone  of  the  scale  with 
a  definite  progression,  it  would,  if  doubled,  bring  about  paral- 
lel octaves.  When  the  fifth,  Fah,  is  doubled,  the  two  Fahs  must 
progress  in  contrary  motion.  The  progression  of  the  fifth,  Doh- 
Soh,  to  the  diminished  fifth,  Te-Fah,  is  allowed,  but  the  reverse 
progression  would  be  an  aggravated  case  of  concealed  fifths,  and 
had  best  be  avoided.  Figure  81.  The  diminished  fifth  is  shown 
by  5th°. 


81. 


.VT                ^-     ^^^~    ^s 

.a*-}        _        J      /^ 

II 

m  —  £-«=- 

S                           & 

.1    „_  (« 

-Gt-^^-O— 

w  —  ^—  .&— 

Good. 

Good. 

Doubtful. 

o            -<51" 

Good. 

pv  « 

H 

2  

2 

_^±  SS  1 

^        -        |J 

5th°      5th  5th        5th<> 


46 


HARMONY  SIMPLIFIED. 


Figure  82,  a  chant  by  Dupuis,  shows  the  vn°  first  with  the 
third,  and  then  with  the  fifth  doubled.  See  also  Figure  52,  the 
seventh  chord. 


T.  S.  DCPUIS. 


82. 


I&    & 

1 

— 

^ 

J         2 

& 

VMy               g 

cj 

z 

m 

^ 

•^ 

-0- 

9 

-p- 

^/ 

^~^  «if 

^        i^ 

^5         1     J^J               ^^ 

M 

1 

1  •iff  /  t 

i 

1 

1 

% 

-^             V  ^ 

Ce 

J^ 

F       U 

j_ 

(S        Si 

1     ^s           \    \^- 

r    p 

r^ 

r 

T 

1    I 

1 

The  character  of  the  chord  is  what  we  should  expect  would 
be  the  result  of  taking  the  strong  steady  Soh  away  from  the  V7, 
and  leaving  the  contradictory  Te  and  Fah.  Although  the  pro- 
gression of  the  chord  is  strong,  the  chord  itself  is  weak.  What- 
ever strength  it  has,  it  derives  from  the  strong  progressive 
tendency  of  Te  and  Fah. 

All  the  chords  last  studied,  that  is,  the  n,  vi,  HI,  vn°, 
may  be  used  in  the  b  position.  The  b  position  is  even 
more  common  than  the  a  position  —  especially  in  the  u,  in, 
and  vn°.  The  c  position  is  very  rare  in  all  of  them,  and 
even  when  found  should  rather  be  regarded  as  an  accidental  com- 
bination of  tones  brought  about  by  the  melodic  progression  of  the 
parts,  than  as  a  real  chord  formation. 


Exercise. 

First.  —  Harmonize  the  bass  given  in  Figure  83. 
Second.  —  Add  the  tenor  and  bass  to  Figure  84. 


E  T 

^^g 


83. 


[   I 


HARMONY  SIMPLIFIED. 


47 


84. 


^—  h^—  )  I  23     gH-—    H 


I 


V 


7d 


»b     V7d 


•35 1 — r<^ n 1 1 1 — i 1 (S? — i 1 n n 


vi     vug   V7c 


Third.  —  Add  soprano,  alto,  and  bass  to  the  following  tenor. 
First  transpose  to  the  key  of  D. 


-     -•-•-•-  m     +-•-  -9-     »-»-»-    -i ^-    m     -&- 

.     -f-  •         -  «  *-f-:F-fi*    « i-.-r — t \--f-  1— 

85. 


m 


vi  IV  V 


7d 


VI   III  VI IK  II 


48 


HARMONY  SIMPLIFIED. 


CHAPTER  XII. 
The  ii,  in,  vi,  and  vno  with  the  Seventh. 

The  V7  is  the  only  chord  of  its  kind  that  is  possible  in  a  key; 
that  is,  it  is  the  only  major  chord  with  minor  seventh  that 
can  be  formed  without  using  tones  foreign  to  the  key.  So  when 
we  hear  such  a  chord  we  know  at  once  what  the  key  is. 


86.  - 


-I  etc. 


''Key:    C. 


E. 


But  other  kinds  of  seventh  chords  may  be  formed  on  the  other 
six  tones  of  the  scale.  The  most  common  of  these  is  the  II7 
(super-tonic  seventh),  formed  by  adding  the  seventh,  Doh,  to 
the  ii  chord.  Figure  87.  This  is  of  course  a  minor  chord  with 
a  minor  seventh.  Its  progression  is  the  same  as  that  of  the  II 
chord,  that  is,  to  the  V,  V7,  or  Ic,  but  it  demands  this  progression 
even  more  strongly  than  does  the  ii  alone.  The  seventh,  Doh, 
should  go  to  Te.  If  the  n  goes  to  the  Ic,  the  Doh  is  stationary, 
but  goes  to  Te  in  the  following  chord  (V  or  V7),  and  the  Te 
in  turn  comes  back  to  Doh.  Figure  87. 


87. 


9t 


m 


"7  V7c 


7d 


All  the  seventh  chords  in  this  and  the  following  chapters 
will  have  the  best  effect  if  the  seventh  is  prepared.  This  is  also 
the  case  with  any  dissonant  tone. 


HARMONY  SIMPLIFIED.  49 

BARNBY.     "  0  Paradise."  GOUNOD.     "3d  Mass." 


88. 


Ho-san-  na    in  the  high  -est. 

3aUj-g44-U4=m: 


vi  n71)V7    I 


'Td 


Figure  89  from  Gade's  "  Aquarellen,"  contains  H7  chords  in 
a,  b,  and  c  position. 

GADE.     "Romance,"  op.  19. 


89. 


j-qit_g_g  >_{=: 


In  the  following  from  Chopin's  "  Barcarolle,"  the  remarkably 
strong  progression  of  the  n7  is  very  plainly  shown. 


CHOPIN.      "Barcarolle." 


90. 


50 


HARMONY  SIMPLIFIED. 


Rule  12.  —  In  all  seventh  chords  the  seventh  should  progress 
or  resolve  down-ward  one  degree. 

For  example,  Fah  to  Me  in  the  V7,  and  Doh  to  Te  in  the  II7. 
It  follows  from  this  that  the  seventh  should  not  be  doubled,  as 
the  result  would  be  parallel  octaves.  The  same  prohibition 
applies  to  any  tone  that  has  a  definite  progression,  as  Te.  See 
Chapter  XI.,  page  45. 

Each  of  the  other  minor  chords  (the  vi  and  the  ni)  may 
be  used  with  the  seventh  added.  Neither  is  of  frequent 
occurrence ;  when  used  they  progress  normally.  Figure  91,  a. 
In  Figure  89,  the  chord  marked  +  is  the  IH7  progressing  nor- 
mally to  the  vi.  In  this  IH7  the  third  is  omitted,  as  we  know  is 
sometimes  the  case  in  the  seventh  chords. 


91. 


Sir  JOHN  STAINER.     "Anthein." 
b. 


Ill        VI-       II 


Figure  91,  5,  from  an  anthem  by  Sir  John  Stainer,  illustrates 
the  use  of  the  VI7.  In  this  case  the  II  also  contains  a  seventh. 
Such  progressions  of  seventh  chords  are  very  common. 

A  chord  of  the  seventh  is  also  formed  on  the  viio,  the 
vil^.  We  may  consider  this  as  either  a  true  seventh  chord  on 
Te,  or,  preferably,  as  a  part  of  the  V7  with  added  ninth.  Its 
progression  is  either  directly  to  the  I  or  through  the  V7  to  the  I. 
Te  goes  to  Doh,  Lah  to  Soh,  and  usually  Fah  to  Me.  If  its  pro- 
gression is  to  the  V7,  Lah  is  the  only  tone  to  move.  Figure 
92,  a. 


HARMONY  SIMPLIFIED. 


51 


MENDELSSOHN. 
b. 


"  St.  Paul." 


92. 


ful^p    =1^= 


°c 


This  chord  is  very  frequently  used,  generally  progressing  to 
the  V?.  In  the  progression  of  vn7a  to  the  Ia  either  the  third  of 
the  I  must  be  doubled  or  we  have  the  parallel  fifths  Ray-Lah, 
and  Doh-Soh,  so  the  progression  to  the  V7  is  preferred. 

These  last  chords  are  of  infrequent  occurrence,  and  the  added 
seventh  weakens  rather  than  strengthens  the  chord  ;  for  it  will  be 
noticed  that  in  each  case  the  three  upper  tones  of  the  seventh 
chords  form  triads  that  are  the  four  strongest  chords  of  the  key. 


Thus  the  VI7  =  the  sub-mediant  tone  +  the  I  chord. 


The  n7  = 


the  super-tonic  tone  +  the  IV  chord.  The  in7  =  the  mediant 
tone  +  the  V  chord.  The  vn7  =  the  sub-tonic  tone  +  the  11 
chord.  In  each  case  the  tone  that  is  trying  to  assert  itself  as 
root  and  bear  up  the  other  tones  as  third,  fifth,  and  seventh,  is 
itself  the  weakest  of  the  four. 

It  will  be  interesting  for  the  student  to  follow  out  in  the  case 
of  these  chords  the  me'thod  used  with  the  chords  studied  pre- 
viously, and  determine  their  character  from  the  character  of  the 
tones  that  compose  them. 

All  the  above  chords  may  be  used  in  the  a,  b,  c,  and  d 
positions. 


Exercise. 

First.  —  "Write  out  all  the  seventh  chords  so  far  studied,  in 
various  positions  and  distributions  with  their  natural  resolu- 
tions (progressions). 


52 


HARMONY  SIMPLIFIED. 


Second.  —  Write  out  the  following  succession  of  chords  in 
any  key  except  C :  V7,  1 1,  vi,  |  vi7,  H7,  |  V,  I,  |  V,  V7d,  I  Ib,  m,  | 
VI,  iibl  I  Ic>  V7d,  I  Ib,  Vc,  |  I,  IVC,  I  I,  n7,  |  Ic,  V7,  1 1.  II 

Third  — Harmonize  the  soprano  melody  given  in  Figure  93. 

The  student  is  again  cautioned  that  he  is  not  expected  to  use 
all  the  chords  that  he  has  studied,  or  even  a  majority  of  them,  in 
writing  an  exercise.  We  have  studied  the  chords  in  the  order  o* 
the  frequency  of  their  use.  The  student  should  use  them  in  the 
same  order. 


93. 


The  following  from  Chopin's  "  Ballade,"  op.  38,  shows  a  series 
of  chords  progressing  normally  but  with  the  seventh  added. 


94. 


^ 


CHOPIN.     Op.  38. 


=t= 


£3 


IV 


HARMONY  SIMPLIFIED. 


53 


CHAPTER   XIII. 

The  I7  and  IVr     Chords  of  the  Ninth,  Eleventh, 
and  Thirteenth. 

Still  another  kind  of  seventh  chord  is  the  major  chord  with 
major  seventh.  It  is  formed  on  the  I  and  on  the  IV.  These 
chords  are  not  often  used  and  are  extremely  harsh.  The  I7 
goes  to  the  IV.  Te  going  down  according  to  Rule  12. 
The  IV7  goes  to  the  V7  (see  Figure  77,  a,  fourth  chord) 
or  Ic .  In  this  last  progression  (IV7  to  Ic)  the  seventh  (Me) 
remains  stationary  through  the  Ic  and  then  resolves.  Figure  95. 
Compare  the  resolution  of  the  H7  to  the  Ic. 


95. 


5 — rg~ 


I7IV      IV7IC 


IV, 


By  continuing  to  build  up  thirds  on  the  V  we  may 
have  the  V7>s,  V7)9jn,  and  V7i9>ii(i3.  The  last  two  can  hardly 
be  called  chords  at  all,  as  they  lack  the  necessary  element  of 
unity  (see  definition  of  chord,  Chapter  I).  They  are  seldom  or 
never  used  in  their  complete  form.  It  is  however  necessary  to 
understand  them  as  certain  combinations  of  tones  are  most  natu- 
rally explained  as  being  these  chords.  The  process  of  building 
up  thirds  must  stop  here,  as  the  last  chord  contains  all  the  tones 
of  the  scale—  the  next  third  would  be  but  the  repetition  of  the 
root,  Soh.  Figure  96. 


54 


HARMONY  SIMPLIFIED. 


The  V7>9,  however,  is  much  used.  In  four-voiced  writ- 
ing the  chord  is  necessarily  incomplete,  the  fifth  usually  being 
omitted.  Te  and  Fah  progress  as  in  the  V7,  and  Lah 
goes  to  Soh.  The  ninth  Lah,  must  always  be  a  true 
ninth,  that  is,  it  must  never  be  a  secefid,  but  must  always  be  at 
least  an  octave  and  one  step  from  the  root,  Soh.  The  seventh 
must  always  be  present  with  the  ninth,  and  the  ninth  is  usually 
in  the  soprano  part.  The  e,/,  and  y  positions  of  chords,  that  is, 
chords  with  the  ninth,  eleventh,  or  thirteenth  in  the  bass,  are 
never  used.  Figure  96  shows  the  most  common  way  of  using 
these  chords. 


96. 


V7,9  V7,9,ll  V7,9,ll,13  V7,9  V7 


7,13 


The  following  are  all  from  famous  compositions  of  acknowl 
edged  masters.  They  illustrate  the  use  of  the  V7  9,  IV7, 
and  V, 


7.13' 


97. 


SCHUMANN.     "To  the  Sunshine."     BEETHOVEN.     Op.  14,  No.  1. 


HARMONY  SIMPLIFIED.  55 

CHOPIX.     ' '  Ballade  in  F. " 


IP 

E3 f tf_llil^ 0     J       J-^l 


j  T"  *  r 

smorzando 


= 


^     "    V7,13 


V7,13  l     V7,13 


CHOPIN.      "  Nocturne,  G  Major." 


/ 


ft\-"- 

1 

•        m            j 

•             1 

• 

^"K    »7        S 

p 

2                     ' 

<?  . 

r: 

-1- 

c\-  ^« 

*  • 

J-  u 

\L 

ivn 


GOUNOD.     "Faust." 


7,13 


Exercise. 

First.  —  Harmonize  the  Soprano  melody  given  in  Figure  98, 
using  the  chords  indicated. 

Second.  —  Write  also  a  second  harmonization  of  the  same 
melody,  using  more  simple  chord  progressions. 


*      • 


-*- — ^ — b^ 


I       iv 


7,9 


iv7   v7    i 


56 


HARMONY  SIMPLIFIED. 


I_J 

tr 

tf 

5 

E! 

• 

V          •>        -ay 

L 

i 

1- 

• 

f 

+  II 

< 

9< 

I 

3*- 
Th 

•! 

(  1  i-j  

TV          V                        V 
lv7b      V7b                  V7d 

ird.  —  Complete  Figure  99. 
K  J     J              I 

r—OTKr*  1  r-*-  —  J  •  —  r™  1  r-J 

~  1  —  1 

»Tb   V7 

in 

ft  —  t 

:  w.  , 

-  —  •  —  ' 

*  S  1 

j 

B 

• 

0  • 

1 

4 

' 

f 

— 

f 

• 

-     i 

r  •     f     \ 

'1 

4 

1 

1 

r      ^    i— 
J  ^J    _J 

IS 

IV7   »7bV7d 

:^— 

m     m       & 

p 

T      1 

4  •          • 

J 

__i 

9 

4 

^r^ 

9~ 

A            \  m  •    u    J 

St^z 

»            i  •            • 

^Tan;  

F—  •  1— 

^              (*  '    r     l*     1 

-^       jl 

i/                  ' 

ff 

.  m               V     1 

III7  VI  ] 

aJt 

1                  1           1 

V7 

V7,9, 

b 

J            f      J 

? 

J        j                   - 

*              •                             ^5            II 

*        •          J 

J 

II 

m 

9 

vi       n7     vug      n 


nib      V7     V7,13 


In  the  fourth  measure  from  the  end,  in  the  vn£  chord,  the 
Te  may  be  doubled  in  the  tenor  part,  since  it  progresses  down- 
ward, the  second  Te  going  to  Doh. 


HARMONY  SIMPLIFIED. 


57 


CHAPTER   XIV. 
Irregular  Progressions.     By-Tones. 

We  have  now  studied  the  formation  and  natural  progression 
of  all  the  chords  that  can  be  formed  within  the  key.  It  would 
be  beyond  the  scope  of  the  present  work  to  attempt  to  follow  out 
irregular  progressions  of  these  chords, —  in  fact  it  would  be  im- 
possible even  in  a  much  larger  work  to  mention  even  a  majority 
of  the  progressions  that  may  be  found.  But  there  are  some  pro- 
gressions that  are  of  such  importance  and  frequent  occurrence 
that  some  notice  must  be  taken  of  them  here. 

First. —  Chords  that  contain  tones  in  common  are  fre- 
quently used  in  place  of  each  other.  Thus  the  vi  for  the  I ; 
the  H  for  the  IV;  the  ni  for  the  V,  and  vice  versa.  Figure  100. 
The  ear  accepts  the  substituted  chord  on  account  of  its  similar 
sound. 


100. 


3=^==| 

<9  G>  I 


1 

:  —  2      i      d       s      i 

-H  i  —  3E  -4- 

)  S*  3  ^j  3  5*  

i         ^      ^       i    i 

-a 

or 

instead  of 

1 

f2           •       (2                                             S3                  £3 

'—{  —  F  —  |  r—  £—  7 

58 


HARMONY  SIMPLIFIED. 


4 


I 


instead  of 


etc.,      or 


etc. 


fl 


=£= 


r 


Second. —  Two  chords  that  contain  two  tones  in  com- 
mon also  frequently  progress  to  each  other.  This  has  been 
well  called  the  passive  progression.  Here  one  tone  takes  the 
place  of  another  for  the  moment,  and  the  idea  of  advancement  is 
subordinate.  The  illustration  will  make  this  plain.  Figure  101. 


101. 


etc. 


33 

^~i             ^~i 

^7                 ^                 /^ 

^ 

-    r<         ex 

-^                S3                 S3 

*<            ,** 

-*.                  ^  ^                   >• 

^•*—  " 

-^_^ 

It  was  said  in  Chapter  II.  that  composition  deals  with  voice 
progression  and  with  chord  progression.  In  such  examples  as 
the  above,  the  single  moving  voice  is  the  point  of  interest.  The 
following  example  from  Wagner's  "  Lohengrin  "  is  a  wonderfully 
beautiful  use  of  this  simple  progression.  It  is  used  at  the  moment 
when  all  action  on  the  stage  ceases  and  Lohengrin  bids  farewell 
to  the  swan.  Figure  102,  a.  Figure  102,  6,  shows  the  progres« 
sion  of  II  to  VI,  and  vi  to  IV. 


HARMONY  SIMPLIFIED.  59 

WAGNER.     "Lohengrin." 


102. 


Fare  -  well, 


fare  -  well,         my       dear  -  est    swan. 


-g- 


-f 


I 


3 

d..  .. 

.1 

^ 

...    & 

II 


MENDELSSOHN.     "St.  Paul." 
6. 


II         VI  IV 


We  may  add,  then,  to  the  progressions  already  studied  tnat 
of  the  V7  or  V  to  vi,  the  V  to  in,  the  IV  to  n  or  to  vi,  the  vi  to  IV 
or  to  I,  the  in  to  V  or  to  I,  the  n  to  VIP,  vii?,  or  to  IV.  The  fol- 
lowing table  gives  the  progressions  of  each  chord  in  about  the 
order  of  the  frequency  of  their  occurrence. 

I  to  any  chord. 

II  normal  to  V.    Also  to  V7,  Ic,  IV,  vno,  vn°. 
in  normal  to  vi.    Also  to  V,  V7,  or  I. 

IV  to  I,  V,  V7,  II,  vi. 

V  normal  to  I.    Also  to  Vi,  in. 
Vi  normal  to  n.    Also  to  IV  or  I, 
Vii°  to  lor  V7. 


60 


HARMONY  SIMPLIFIED. 


The  addition  of  the  seventh  to  any  one  of  these  chords 
strengthens  its  tendency  to  make  the  normal  progression. 
Chords  in  the  b  position  move  much  more  easily  to  the  unusual 
progressions  than  when  they  are  in  either  the  a  or  the  c  position. 

Seventh  chords  may  move  to  other  seventh  chords. 

When  one  voice  moves  to  some  other  tone  of  the  same 
chord,  the  other  voices  remaining  stationary,  such  inter- 
mediate tone  is  called  a  by-tone. 

Rule  13. — A  by- tone  must  be  a  tone  of  the  chord,  not  some 
new  tone,  and  must  appear  on  the  unaccented  part  of  the  beat 
or  measure.  Figure  103,  a,  c,  d.  The  figure  so  frequently  used 
in  accompaniments  called  "  broken  chords "  is  a  common  ex- 
ample. 


103. 


+ 


1 


HOFMANN.     "Melusina." 


/T  h   u  /  »                iv 

•                                ^ 

a. 

in\  ocE 

i                ~-m                   ^ 

fin                  « 

!                1                  2              ' 

C                 ."" 
Is 

c                • 

1  •      I/       /  4                    M 

i                *                   i 

-^     1*     i-  »   J                    i 

i                                             M 

J                • 

"     7                          C 

b                     F 

•                •                   | 

P 

HUMMEL.     Op.  55. 


+ 


jLjLJt 

-N-i 1 1 — 


*  J_    J*    ^ ^ 

^^1 


HARMONY  SIMPLIFIED. 


61 


MOZART.      "  Symphony  in 


In  Figure  103,  6,  although  the  new  tone  really  forms  a  differ- 
ent chord,  the  V7,  it  is  customary  to  regard  it  as  a  by-tone.  The 
notes  marked  with  an  +  in  Figure  103,  e,  f,  and  g  are  all  by-tones. 
Two  voices  may  take  by-tones  at  the  same  time,  the  other  voices 
remaining  without  progression.  Figure  104,  a,  b. 


1O4. 


d. 


•& '-I * — L-s* *— 1 *—t-      —I *-• 

*  I      I      I      I 

Bad.  Bad. 


At  Figure  104,  c,  although  both  the  tones  F  and  B  are  in  the 
same  chord,  the  V7,  the  progression  of  the  soprano  is  not  good. 
The  interval  is  the  augmented  fourth,  and  any  augmented  or 
diminished  interval  is  not  suitable  for  a  melodic  progres- 
sion :  see  also  Figure  104,  d,  e. 


Exercise. 

First. — Harmonize  again  the  melody  in  Figure  98  and  make 
the  seventh,  thirteenth,  and  twenty  -first  notes  by-tones. 
Second.— Complete  Figure  105. 


62 


HARMONY  SIMPLIFIED. 


1O5. 


J 


J  _i 


VIvI  I 


7,9,11. 


•5- 


u 


=Efc 


Notice  how  much  greater  freedom  the  use  of  by-tones  gives 
us.  In  the  first  measure  are  two  by-tones.  Beginning  at  the 
ninth  measure  the  tenor  imitates  the  soprano  of  the  first  four 
measures. 

Third.— Complete  Figure  1O6.  The  notes  marked  4-  are  by- 
tones. 


106. 


E^= 


m 


~8: 


II 


HARMONY  SIMPLIFIED. 


63 


CHAPTER   XV. 
Review. 

Before  taking  up  the  study  of  modes  and  keys,  it  will  be  well 
for  us  to  pause  here  and  consider  what  material  we  already  have. 

We  have  formed  triads  and  seventh  chords  on  each  of  the 
seven  tones  of  the  scale,  giving  us  fourteen  chords.  Each  chord 
may  be  used  in  the  b  position,  giving  us  fourteen  more.  Each 
may  be  used  in  the  c  position,  though  with  many  this  is  rare, 
giving  fourteen  more.  Each  seventh  chord  may  be  used  in  the  d 
position,  giving  seven  more.  In  addition  we  have  the  ninth, 
eleventh,  and  thirteenth  chords  in  various  positions,  and  also  the 
use  of  by-tones.  When  we  consider  that  all  these  chords  may 
be  written  in  any  one  of  twelve  keys,  and  in  an  endless  variety  of 
distributions,  it  will  be  seen  that  we  have  already  sufficient  ma- 
terial to  enable  us  to  do  a  great  deal.  The  student  should  read 
again  the  remarks  in  Chapter  VII,  and  then  carefully  review  the 
following  chapters  up  to  the  present.  By  this  means  many 
points  will  become  clearer. 


Exercise. 

First.  —  As  an  exercise  take  the  melody  of  Figure  1O7,  and 
use  it  first  as  a  soprano,  then  as  an  alto,  then  as  a  tenor,  and  fi- 
nally as  a  bass,  transposing  so  as  to  make  the  compass  of  the 
voices  convenient,  and  add  the  three  remaining  parts  in  each 
case.  Quarter  notes  as  by-tones  may  be  used  wherever  effective. 


64 


HARMONY  SIMPLIFIED. 


The  harmonizations  should  be  written  in  several  ways,  in  one 
using  only  the  simplest  chords,  in  another  introducing  some,  not 
many,  of  the  more1  unusual  chords  and  progressions. 

Below  are  given  the  possible  harmonizations  of  each  tone  of 
the  scale  when  the  soprano  is  given.  The  various  positions  are 
omitted. 


108. 


—Jf-  55  <S»  

-«&  

I                ii               in             IV 

V                vi              vii°. 

I7               n7             in7           IV? 

V?              v,T            v«o 

VI                     VII°                   I                       II 

v7(9       iv          v7 

vi7            vn§             I7              n7 

V7,ll         IV7             V7,9 

IV              V               vi             vn° 

V7,13          »                 V7,ll 

IV,             V,              vi,           vn? 

n7          v7)13 

n7             in7             IV7           V7 

in7         v7)9       v 

V                                         V                  V 
V7,ll                                  7,13          V7,9 

vi?            vno            ,„ 

V 


7,11 
r7,13 


Second.  —  Write  out  a  similar  table  of  the  possible  harmo- 
nizations of  the  tones  of  the  scale  when  the  bass  is  given. 

Third.  —  Harmonize  Figure  109.  In  one  place  the  progression 
indicated  is  slightly  different  from  that  given  in  the  text. 


rr- 


VI    IV    IK      V 


7.1 


Fourth.  —  Analyze  the  hymn  tune  called  "  Missionary  Hymn," 
marking  with  the  proper  numerals  all  the  chords  that  we  have 
studied. 


HARMONY  SIMPLIFIED.  65 

CHAPTER   XVI. 
The  Minor  Mode. 

We  have  seen  in  Chapter  VIII  that  the  three  minor  chords  of 
a  key  have  the  same  relation  to  each  other  as  the  three  major 
chords.  If  this  relation  is  emphasized  and  the  three  minor  chords 
are  made  the  most  important  and  the  three  major  chords  are 
made  subordinate,  the  minor  mode  is  produced ;  minor  meaning 
secondary  or  subordinate,  and  mode  meaning  the  manner  or 
method  of  using  the  chords.  It  is  important  to  remember  that 
the  character  of  the  chords  is  unchanged,  the  minor  chords  are 
still  sorrowful  in  character,  the  major  bright  and  bold,  but  the 
whole  character  of  the  composition  is  governed  by  the  minor  and 
not  by  the  major  chords  as  formerly.  This  is  because  the  minor 
chords  are  given  greater  prominence  and  the  major  chords  less. 

The  vi  now  becomes  the  central  chord,  and  is  a  minor  tonic, 
to  which  the  in  is  a  dominant  and  the  11  a  sub-dominant. 
So  the  chord  on  Lah,  formerly  the  vi,  we  now  call  the  I,  that  is, 
the  minor  tonic ;  the  former  ill  is  v,  and  the  n  is  now  iv.  Now, 
the  tonic  character  of  this  new  tonic  is  greatly  strengthened  if  we 
make  the  new  dominant  (in  of  the  major  mode)  a  major  chord  by 
changing  Soh  to  Se.  Figure  110,  a.  This  is  almost  invariably 
done,  as  the  ill  is  a  very  weak  chord,  and  here  we  require  a  strong 
chord  if  it  is  to  have  the  dominant  character.  Our  chords  will 
now  be :  — 

iv  i  V 


A 


Ray          Fah         Lah        Doh         Me         Se         Te 

4  ^  -*•  3,          f  1 

•f  2  »  v?    •         &  i. 

Forming  a  scale  of  the  tones  of  these  chords  we  have :  Lah, 

Te,  Doh,  Ray,  Me,  Fah,  Se.  This  is  called  the  harmonic 
minor  scale.  We  may  form  chords  on  each  degree  of  this  scale 
exactly  as  we  did  with  the  major  scale.  Figure  110,  b. 


66 


110. 


HARMONY  SIMPLIFIED, 
b. 


As  Lah  is  now  the  tonic  tone,  we  regard  it  as  the  key  note  of 
the  minor  mode,  just  as  Doh  is  the  key  note  of  the  major  mode. 
Thus,  if  C  is  Doh,  our  key  is  either  C  major  (mode)  or  A  minor 
(mode),  according  as  we  use  Doh  or  Lah  as  tonic.  The  two 
keys  are  written  with  the  same  signature,  and  are  said  to  be  each 
the  relative  of  the  other ;  as,  A  flat  major  the  relative  major  of 
F  minor,  or  A  minor  the  relative  minor  of  C  major,  or  G  the  rela- 
tive major  of  E  minor. 

The  chords  formed  on  the  minor  scale  are  used  very  nearly  as 
are  the  corresponding  chords  in  the  major  scale.  Thus  the  I  (on 
Lah)  is  used  precisely  as  the  I  (on  Doh).  The  V,  V?  and  IV 
are  used  just  as  the  corresponding  chords  in  the  major. 

The  interval  from  Fah  to  Se  is  an  augmented  second ;  as 
stated  in  Chapter  XIV,  augmented  and  diminished  intervals  are 
not  good  melodic  intervals,  so  we  will  avoid  the  progression 
of  Fah  to  Se.  Figure  110,  c. 


Exercise. 

First.  —  Harmonize  the  following  bass.    When  complete  com- 
pare the  result  with  Figure  41. 


V    V     i 


HARMONY  SIMPLIFIED. 


67 


Second.  —  Complete  Figure  111,  b. 

Third.  —Transpose  the  bass  thus  completed  into  c  minor  and 
write  new  upper  parts. 


111.  b. 


The  use  of  the  b  and  c  positions  in  the  minor  mode  is 
the  same  as  in  the  major,  but  as  the  i  and  iv  are  here  minor 
chords,  the  third  may  be  doubled  even  in  the  b  position. 

Figures  112  and  113  illustrate  the  i,  V,  and  iv  in  the  minor 
mode. 


112. 


HANDEL.     "  Acis  and  Galatea. ' 

^ 

N 


v  r 

,-        J-       I*     £ 

iH 


4i  *   fe: 


1 


Moderate. 


Y     'b      Iyb  Ivb   V 


GURLITT.     Op.  117. 


U3. 


«.-     i 


IT        V 


68 


HARMONY  SIMPLIFIED. 


CHAPTER   XVII. 
The  Minor  Mode  Continued. 

It  will  be  found  that  in  the  minor  mode  there  is  always  a  ten- 
dency to  revert  to  the  major  mode.  The  minor  mode  is  more 
artificial  than  the  major,  and  the  minor  chords  are  weaker  than 
the  major,  so  that  it  requires  a  constant  effort  to  make  the  minor 
mode  appear  the  basis  of  the  composition.  This  is  found  to  be 
especially  true  when  we  attempt  to  use  the  mediant,  sub-mediant, 
major  sub-tonic  (using  Soh  instead  of  Se),  in  the  minor  mode. 
These  three  chords  are  the  I,  IV,  and  V  of  the  major  mode,  and 
must  be  used  very  sparingly  or  the  feeling  of  the  minor  mode  is 
lost.  By  referring  to  Figure  110,  6,  we  find  that  if  Se  is  used 
as  the  seventh  of  the  scale,  the  III  becomes  III+,  a  major  chord 
with  augmented  fifth  (the  augmented  fifth  indicated  by  the  + 
sign),  and  the  sub-tonic  becomes  a  diminished  chord.  As  Se  is  a 
necessity  if  we  are  to  have  a  leading  tone,  the  chords  as  shown 
in  Figure  110  are  the  usual  ones  in  the  minor  mode.  But  the 
forms  with  Soh  instead  of  Se  also  occur.  This  is  shown  by 
the  following,  Figure  114.  The  Soh  is  most  likely  to  occur  when 
it  progresses  to  some  tone  other  than  Lah,  and  hence  the  need  of 
a  leading  tone  is  less  felt.  See  also  Figure  129,  c. 


114. 


GRIEG.     "  Sonata,"  Op.  7. 


G:  I, 


VI    '    V  1 6:  i.  V 


nr 


VI  VI 


HARMONY  SIMPLIFIED. 


Op.  1. 


ZBLTER.     "  Der  Konig  in  Thul*." 


c:V     i  III"     *c         -•-  a:  i      v      VI  iv    V 

The  III+  is  rarely  used  in  simple  four-part  writing.  When 
used  it  progresses  to  the  VI  as  in  the  major  mode,  tnat  is,  the 
normal  progression.  Se  must  progress  to  Lah.  Figure  116,  a. 
The  chord  is  often  used  with  the  fifth  omitted,  thus  evading  the 
difficulty.  See  Figure  117,  last  chord. 

The  VI  is  here  a  major  chord.  It  progresses  to  the  n°  or  IJ°  as 
in  the  major  mode,  although  the  progression  cannot  be  called  normal 
since  the  n°  is  not  a  perfect  fifth  below  the  VI.  Figure  11 6,  b. 

The  vii°  precisely  as  in  the  major  mode.     Figure  116,  c?. 

The  11°  (on  Te)  is  here  a  diminished  chord,  but  is  us^d  just 
as  the  II  (on  Ray)  in  the  major  mode,  unless  perhaps  the  a  posi- 
tion is  more  rare.  As  Te  is  no  longer  the  leading  toca  it  is  free 
(o  move  either  up  or  down  or  by  a  skip.  Figure  116,  b. 

HANDEL.     "  Messiah." 

_J_M    _l     -U 


115. 


116. 


^-g---^-     f*      J- 


III      III+  VI     VI    ng 


70 


HARMONY  SIMPLIFIED. 


MENDELSSOHN.     "  St.  Paul." 


117. 


tas 


F 


f:        VI 


vi 


118 


Exercise. 
First. — Harmonize  the  folio-wing  bass. 

a. 


:B 


Pi 


in 


=F 


VII         V 


fl 


-0 0- 


Second. — Harmonize  the  folio-wing  soprano. 


J    U ,  !  J 


i 


m   m+vi  ng  ic      v7oi 


HARMONY  SIMPLIFIED.  71 

CHAPTER   XVIII. 
Minor  Mode  Concluded. 

The  use  of  the  seventh  chords  in  the  minor  mode  varies  but 
little  from  their  use  in  the  major  mode.  All  the  harmonies  on 
the  dominant,  that  is,  the  V7,  V7  9,  V7  g  n,  V7  9  n  13,  are  only- 
found  when  the  dominant  is  made  major,  and  are  then  used  as  in 
the  major  mode,  but  the  chords  themselves  are  slightly  different 
in  their  form.  The  V7  is  the  same  in  both  modes,  and  the  reso- 
lution of  the  third  (Se)  and  the  seventh  (Ray)  is  the  same, 
only  Ray  moves  down  a  whole  step  to  Doh,  whereas  in  the  major 
mode  the  seventh  of  the  V7  (Fah)  moves  down  a  half  step  to 
Me. 

The  V7  9  is  used  as  in  the  major  mode,  but  the  ninth  (Fah)  is 
a  minor  ninth,  resolving  downward  a  half  step. 

The  V7  n,  or  V7  9  n,  is  rare,  but  is  used  as  in  the  major  mode. 

The  V7  13,  which  is  about  the  only  form  in  which  the  chord  of 
the  thirteenth  occurs,  is  used  as  in  the  major  mode,  the  thirteenth 
being  here  a  minor  interval. 

The  iij  is  very  frequently  used,  and  in  the  same  way  as  in  the 
major  mode.  Figure  119,  d. 

The  VI7  and  the  III+  are  used  as  are  the  corresponding  chords 
in  the  major  mode.  Figure  119,  a,  t>. 

The  Ij7,  that  is,  the  minor  chord  on  Lah  with  the  major 
seventh  Se  added,  is  so  extremely  harsh  as  not  to  be  used.  The 
i7  (with  Soh)  is  used  progressing  to  the  IV. 

The  i\T7  (here  a  minor  chord  with  minor  seventh)  is  much 
more  frequently  used  than  the  corresponding  IV7  in  the  major 
mode.  It  is  much  more  pleasant  to  the  ear,  and  is  of  considerable 
importance.  It  progresses  to  the  V7  or  ic.  Figure  119,  c.  No- 
tice that  its  tones  are  the  same  as  those  of  the  H7  in  the  major 
mode.  (Ray,  Fah,  Lah,  Doh.) 


72 


119. 


HARMONY  SIMPLIFIED, 
b.  c. 


a:  VI?b       no         m+      VI 


d. 


IV7  V7 


1  

if"r\       ^^           **<**             ^^ 

&< 

V--  L/       ^^           ff^3             ^^ 

&         *      &              <y 

or 

or 

-g^ 

^~"^  • 

'  1    Jt^               2             tt 

^                                 II 

^r~  

—  «  a 

H 

TIO                     V                         TT° 

"7             V7c           "7 

T                               VTlO                      V 

ic              .n7           v? 

II 

"'?      I 

The  VH°.  is  used  as  the  corresponding  chord  in  the  major  mode, 
but  it  is  a  much  more  important  chord.  It  is  known  as  the  chord 
of  the  diminished  seventh,  that  being  the  interval  formed  by 
the  extreme  tones  of  the  chord.  Figure  119,  e.  We  shall  find 
later  that  it  is  borrowed  for  use  in  the  major  mode,  and  is  of  the 
greatest  use  in  moving  from  one  key  to  another. 

The  minor  mode  is  frequently  a  source  of  great  trouble  and 
misunderstanding  to  students  of  harmony,  but  if  the  following 
principal  facts  are  kept  in  mind  there  need  be  no  trouble. 

First.  The  minor  mode  is  but  a  shadow  or  an  echo  of 
the  major  mode,  since  it  is  made  from  it  and  resembles  it 
greatly. 

Second.  The  chords  of  the  minor  mode  have  the  same 
names  and  are  used  almost  exactly  as  the  corresponding 
chords  of  the  major  mode.  In  the  key  of  A,  for  example, 
whether  the  mode  be  major  or  minor,  the  chord  on  A  is  the  tonic, 
and  is  so  used, — and  the  same  is  true  of  most  of  the  other  chords. 
In  fact,  many  compositions  written  in  the  major  mode  would  be 
just  as  correctly  written  if  the  signature  were  changed  to  that  of 


HARMONY  SIMPLIFIED. 


73 


the  parallel  minor,*  care  being  taken  to  introduce  the  sharped 
seventh  of  the  scale  as  an  accidental.  Figure  120,  a,  is  equally 
good  in  either  mode. 

a.  Convertible  Chant.     HOPKINS. 


120. 


/ 


i 


Exercise. 
First. — Harmonize  Figure  12O,  b. 


& 

& 

I 

ft)        V\  i     £         j 

^       5*      ^5 

•    «       /-^ 

•  1    -<s> 

•  * 

«J                       * 

i 

^2         ^D 

[               P' 

* 

U    \)      '    " 

i 

v 

1      l     1 

7,9,11 

| 

=    J 

V 

1  i 

7< 

1 

J     | 

l« 

f        * 

j          J 

A     |  <^ 

,   ± 

I 

> 

3    0 

1  1 

/5  s_K           82 

^    d  \  & 

3 

^ 

2    • 

•z>    1 

irrS    "  2 

9—  - 

II 

y\  ^7                 ^^ 

L 

E 

H 

p\«    u 

P 

b  b 

1 

i,obIIIbVI 

]7c                 HI 

ir  in 

b 

V7,13 

*  The  minor  mode  on  the  same  key  —  changing  Doh  to  Lah.     Thus,  G  major 
(key  of  one  sharp)  is  the  parallel  of  G  minor  (two  flats). 


74  HARMONY  SIMPLIFIED. 

Second. — Harmonize  the  folio-wing  bass. 


V7bV7,13V7»?c     V7d 





Third. — Harmonize  the  following  according  to  the  harmonic 
basis  given. 


122. 


— Z5i- 


i  iv,,       i         VI          iv 


!„         V        V,      VI 


4 4- 


II 


V7        l         VII7b     Jb       IV 


V        V 


Fourth. — "Write  the  same  melody  in  A  major  and  harmonize 
it,  comparing  the  chords  in  the  two  modes  when  complete. 

The  following  illustrates  the  use  of  some  of  the  chords  of  the 
minor  mode.  Figure  123. 


CHOPIN.     "Nocturne,"  No.  11. 


123. 


g:  i  vno          vi  vnObv  VI  ib     "7  V7  l 


HARMONY  SIMPLIFIED. 

MENDELSSOHN.     Op.  22, 


i 
I 


t=t5a= 


=^: 


s=5= 


HI 


£=£ 


:i= 


^B 


&:  iv  b 


GOUNOD.     "There  is  &  Green  Hill." 


He    died    that  we    might  be  for-given,    He   died        to  make   us    good. 


±=&- 


\=r-  *-•— \-r- 

*,     *:    ~5       d   ii~^    ~>» j     j 

^8=i=J35^t*l=^^= 


S 


r 


-*--- 


-_  ^  - — 

r         r 


76  HARMONY  SIMPLIFIED. 

CHAPTER    XIX. 
Transition  or  Modulation. 

By  key  is  meant  the  tone  on  which  the  tonic  is  based, — 

in  the  major  mode,  Doh ;  in  the  minor  mode,  Lah.  Thus  a  com- 
position is  in  the  key  of  G  major  if  the  tonic  chord  is  based  on 
G,  and  is  a  major  chord. 

When  any  chord  other  than  the  original  tonic  assumes  the 
character  of  tonic,  we  have  a  transition  or  modulation  to  some 
other  key  or  mode.  A  change  of  key  is  properly  called  a  tran- 
sition, and  a  change  of  mode  a  modulation,  but  the  latter  word  is 
frequently  used  to  express  either  idea.  If  the  idea  of  the  new 
tonic  is  sufficiently  strong  to  replace  the  old  tonic  completely,  the 
transition  is  complete.  If  the  new  tonic  is  simply  suggested, 
the  transition  is  passing. 

To  produce  a  transition,  a  chord  that  is  unmistakably  in  the 
new  key  must  be  introduced.  For  example,  a  new  Ic  or  V?.  As 
soon  as  one  of  these  chords  is  used,  all  the  following  chords  must 
be  treated  as  belonging  to  the  new  key.  A  transition  is  brought 
about  most  smoothly,  if  some  chord  that-  is  common  to  both  keys 
(called  a  bridge  chord)  is  used  just  before  the  characteristic 
chord  of  the  new  key.  For  example,  in  going  from  the  key  of  C 
to  the  key  of  G,  we  may  use  the  vi  of  C  as  a  bridge-chord,  and 
follow  it  by  the  Ic  or  V7  of  the  key  of  G.  Figure  124,  a.  In 
this  case  the  vi  of  C  is  composed  of  the  same  tones  as  the  n  of 
G,  and  we  treat  it  as  if  it  were  a  n. 

In  Figure  124,  b,  from  Beethoven's  "Sonata  Pathetique,"  we 
have  precisely  the  same  use  of  chords.  Here  the  transition  is 
from  the  key  of  AJJ  to  the  key  of  EJJ,  the  bridge-chord  being  the 
minor  chord  on  F. 

Another  common  bridge-chord  is  the  Vc  used  as  Ic.  See 
Ihymn  tune  "  Duke  Street,"  first  cadence.  Any  triad  of  the  scale 


HARMONY  SIMPLIFIED.  77 

(except    vii°)  may  be    used   in   the    same  way..    See  "  Regent 
Square,"  third  cadence  for  vic  used  as  Ic. 

BEETHOVEN.     "  Sonata  Pathfetique." 
b. 

nt 


124. 


I 


7d 


J-. 


^-t^—  j                 t  —  [-                t. 

•j-  hj^j)  —  H 

Ck-    k   * 

bjilfi  b     J                            1 

Z_E-fi2    • 

J 

"9   V                                           j 

e        J 

•        * 

Tb                          V7b 

I           V          vi 

Eft:  ii           Vr 

tn                *- 

Rule  14.  —  The  chromatic  alteration  of  a  tone  must  occur  in 
the  same  part  or  voice. 

That  is,  if  G  is  in  the  soprano  part  in  one  chord,  and  Gjjt 
appears  in  the  next  chord,  the  G^t  must  also  be  in  the  soprano 
part.  Figure  125,  a.  To  show  the  possibilities  of  transition  by 
means  of  a  bridge  chord,  take  the  chord  of  C.  This  is  the  I  in 
C,  the  IV  in  G,  the  V  in  F  or  in  F  minor,  and  the  VI  in  E 
minor.  Hence  we  could  use  it  in  going  to  any  of  these. keys. 

Transitions  are  also  made  without  the  use  of  a  bridge  chord, 
generally  by  using  two  tones  or  even  a  single  tone  that  is 
common  to  both  keys.  For  example,  we  may  go  from  the  key 
of  C  to  the  key  of  Ap  by  using  the  tone  C,  first  as  the  root  of 
the  I,  and  then  as  the  third  of  the  chord  on  Ap,  and  treat  this 
last  chord  as  a  I.  Figure  125,  b.  . 


78 


HARMONY  SIMPLIFIED. 


125. 


BEETHOVEN.     "  Andante  Favori." 


Z>t>:  I  V       I 


Figure  125,  <?,  shows  a  similar  transition  from  F  to  Dj?. 


Exercise. 

First.  —  Harmonize  the  folio-wing.    "Write  in  duple  time. 

C:  I,  V,  |  I,  Ib,  I  IV,  IVb,  |  I,  I  I,  V7,  II,  vi,  |  G:  IC,"V7,  | 
I,  C:  IV,  V7C,  |  I,  I,  |  a:  VI7,  ivb>  |  V,  |  C:  I,  V7,  |  vi,  IV,  | 
P :  Vb,  V7b,  |  I,  |  C :  V7C,  I,  |  I,  Ib,  |  Ic,  V7,  |  I.  II 

In  distinguishing  the  keys,  C  (capital  letter)  means  the 
key  of  C  major,  c  (small  letter)  means  the  key  of  c  minor. 

In  the  above  exercise  the  student  will  notice  that  there  are 
five  cadences;  the  first  in  C,  the  second  in  G,  the  third  in  A 
minor,  the  fourth  in  F,  and  the  last  in  C.  It  is  veiy  common  to 
strengthen  a  cadence  in  this  way,  that  is,  by  making  the  last 
chord  of  a  cadence  sound  like  a  tonic.  We  thus  contrast  keys 
instead  of  single  chords. 


HARMONY  SIMPLIFIED. 


79 


Second.— After  writing  the  foregoing  exercise,  write  anew 
one  as  follows  :  First,  a  simple  melody  in  half  notes  and  quarter 
notes,  sixteen  measures  long,  in  either  duple  or  triple  time, 
composed  of  four  phrases  of  four  measures  each,  a  cadence  at 
the  end  of  each  phrase.  Figure  120,  />,  may  be  used  as  a  model. 
Make  the  first  cadence  to  the  I  either  perfect  or  imperfect ;  the 
second  to  the  V,  using  a  transition  to  that  key  :  the  third,  a  sim- 
ilar transitional  cadence  to  the  IV ;  and  the  last  a  strong  perfect 
authentic  cadence  to  the  I.  In  this  exercise  the  student  for  the 
first  time  furnishes  all  the  material.  He  will  succeed  best  if  he 
aims  at  simplicity  rather  than  at  "  effect." 

Figure  124,  I,  shows  a  transition  to  the  key  of  the  V.  Fig- 
ure 125,  <?,  gives  one  to  the  key  of  the  f>VI.  Figure  126,  a,  gives 
one  to  the  key  of  the  in.  Figure  126,  b,  gives  one  to  the  key  of 
the  IV. 


KULLAK.     "  Octave  Study." 


126. 


Efe 


m 


II 


F:  I  vi, 


13 


SCHUMANN.     "Grillen.' 


;gl  2 

s?  •                          •     »              •, 

l| 

J 

:S 

: 

te*5»         -*»s  -*         + 

f~\'    K  i 

ii 

ri«.  £^k 

2f  fiuP 

1 

, 

v7d  ib        v7c 


80 


HARMONY  SIMPLIFIED. 


Third.  —  Harmonize  the  following.    It  is  the  bass  of  a  well 
known  hymn-tune. 


127. 


I     !„  I> 


F:nIcV, 
:  !„   V       V.  iu  i 


HARMONY  SIMPLIFIED.  81 

CHAPTER   XX. 
Altered  Chords. 

There  are  four  ways  of  using  tones  that  do  not  belong  to  the 
scale  of  our  key : 

First. — By  changing  the  key.  This  we  have  spoken  of 
in  the  preceding  chapter  on  transition. 

Second. — By  using  altered  chords. 

Third. — By  chromatic  chords. 

Fourth. — By  mixed  chords. 

To  understand  the  second  and  third  classes,  we  must  remem- 
ber that  every  chord  possesses  two  characters :  First,  the  character 
that  is  determined  by  its  form,  whether  major,  minor,  diminished, 
etc.,  which  is  independent  of  key  and  which  we  may  call  its 
formal  character.  Second,  the  character  that  is  determined  by 
its  relation  to  other  chords,  whether  tonic,  super-tonic,  etc.,  which 
for  want  of  a  better  name  we  may  call  its  degree  character. 

Any  change  in  a  chord  effects  its  formal  character,  but  it  is 
possible  to  change  one  of  the  tones  of  a  chord  without  destroying 
its  degree  character.  Thus  we  may  make  a  major  sub-dominant 
into  a  minor  sub-dominant,  and  it  will  be  a  sub-dominant  chord 
still,  though  its  form  is  changed.  Figure  128,  a.  Chords  so 
changed  are  called  altered  chords.  They  are  used  nearly  as  are 
the  chords  from  which  they  are  formed.  The  major  dominant 
that  we  use  in  the  minor  mode  is  really  an  altered  chord. 

The  following  are  the  most  common  altered  chords.  Notice 
that  any  tone  of  the  chord  except  the  root  may  be  changed. 

The  I  may  be  made  minor. 

The  i  may  be  made  major.      Figure  128,  b. 

Either  may  be  changed  to  a  major  chord  with  augmented 
fifth.  These  chords  are  used  just  as  before  alteration,  except 
that  the  sharped  tone  must  progress  upward  a  half-step.  Figure 
128,  c,  and  Figure  129,  d. 


82 


HARMONY  SIMPLIFIED. 


The  ii  may  be  made  11°  and  the  reverse  without  change  in 
their  use.  So  too  with  the  H7  and  the  ii^.  Figure  128,  d. 

The  IV  may  be  made  minor  and  the  iv  made  major  without 
change  in  their  use.  Figure  128,  a. 

The  IV  or  the  V  may  have  the  fifth  augmented,  the  fifth 
moving  up  a  half-step. 

The  ninth  in  the  V7  9  may  be  flatted  in  the  major  mode  or 
sharped  in  the  minor  mode.  Used  as  before  alteration.  Fig- 
ure 128,  e. 

The  fifth  in  the  V7  maybe  either  raised  or  lowered  a  half -step. 

The  vn^  in  the  major  mode  and  the  11°  in  the  minor  mode 
may  have  the  seventh  flatted,  giving  the  chord  of  the  dimin- 
ished seventh.  Figure  128,/. 


128. 


I        iv 


r,       V-      I  i   or    I         1+     IV 


This  changing  of  major  chords  to  minor  and  the  reverse  pro- 
duces the  effect  of  mingling  the  two  modes.  Many  beautiful  ef- 
fects are  produced  in  this  way  by  modern  writers.  Figure  129. 


HARMONY  SIMPLIFIED. 


83 


Chopin.     "Nocturne,"  No.  11.         Schubert.     "  Minuet,"  from  op.  78. 
a.  b. 

yfcB= 


129. 


IV     iv  ^ 


V       I 


CRAMER.     "Study." 


-P — i- 


I 


MENDELSSOHN.     "Capriccio,"  op.  22. 
d. 


G:  I        1+  vi 


34  HARMONY  SIMPLIFIED. 

Exercise. 

First.— Harmonize  the  following. 


13O. 


'7b 


VV+ 


Second.— Also  the  following. 


III     III     vi       n°c 


IV 


vi        nb     nb 


7c 


Third.— Complete  Figure  132. 


132. 


fOyt'   9                I 

^       • 

0  — 

^ 

3     . 

X^Z_                        rf-l  

J 

i 

~  1 

n7b     u7    V7 


VI1b°7c 


i 


C:  V 


VTd  C:nTd 


HARMONY  SIMPLIFIED. 


85 


3H^§3S 

±£*=  £&-!«=•= 


^M 


1 


^i 


-p— ^~- 


IV     IV7    iib  V7>9 


HARMONY  SIMPLIFIED. 


CHAPTER  XXI. 
Chromatic  Chords. 

In  a  chromatic  chord  both  the  formal  and  the  degree  char- 
acter of  the  chord  have  been  changed  so.  that  the  chord  appears 
as  if  borrowed  from  some  other  key ;  but  it  differs  from  a  tran- 
sitional chord  in  that  it  must  progress  to  some  characteristic 
chord  of  the  original  key.  The  characteristic  chords  of  a  key 
are  those  that  belong  unmistakably  to  that  key  only,  that  is,  the  Ic 
and  V7.  For  example,  if  the  II7  is  made  II7,  its  character  both 
as  a  minor  chord  and  as  a  super-tonic  chord  is  lost.  If  it  pro- 
gresses to  the  V  it  produces  the  effect  of  a  new  key,  and  we  say 
that  it  brings  about  a  transition.  If,  however,  it  progresses  to 
the  Ic  or  V7,  either  of  these  chords  strongly  contradicts  any  tran- 
sitional tendency,  and  we  call  the  chord  chromatic.  In  the 
first  case  the  chords  are  lettered  in  the  new  key  (that  is  V7,  I). 
Figure  133,  a.  In  the  second  case  the  chords  are  lettered  in  the 
original  key  (that  is  II7,  Ic  or  V7,  I).  Figure  133,  b. 


133. 


ft 

|              1 

L/ 

1-    J             j 

j/f"            ^x                  £x 

«                 (5? 

^ 

\Cl")            J               JtriJ 

|           it/-J 

- 

1  

1               -(2- 

: 

? 

2 

<~V       I               r 

CS?       1  P 

\                      £ 

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t 

C:  vi 
C:  ii             \ 

T 

1 

C:  vi            II7 
I 

I 

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r 

I 

HARMONY  SIMPLIFIED. 


87 


vr 

fn\ 

sa            -a 

W                     Li    i 

^—  a—  h 

54  _  &  

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z      i 

i15'             1 

o                     ^^ 

a 

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(7:  vi 

I 
II7              V7 

i 

r 

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i 

Transitional  chords  change  the  key.  Chromatic  chords 
try  to  change  the  key  but  are  not  allowed  to  do  so.  Al- 
tered chords  contain  tones  foreign  to  the  key,  but  no 
change  of  key  is  thought  of.  Figure  133,  a,  b,  c,  shows  re- 
spectively transitional,  chromatic,  and  altered  chords. 

The  most  common  chromatic  chords  are  II,  II7,  II7  9,  $iv°, 
$IV7,  tjlivb7,  all  of  which  must  progress  to  the  Ic  or  V7.  The 

jj|iv0  is  the  I V  with  its  root  raised  a  half  step  from  Fah  to  Fc, 
thus  making  a  diminished  chord.  The  tiiv^  gives  us  another 
form  of  the  diminished  seventh  chord.  We  see  from  these  chords 
that  the  root  of  a  chord  may  be  changed  to  produce  a  chromatic 
chord.  This  was  not  the  case  with  an  altered  chord.  The  follow- 
ing shows  various  chromatic  chords.  The  student  should  com- 
plete the  progressions  through  to  the  I  chord.  The  last  example, 
Figure  134,  /,  shows  a  major  mediant  progressing  to  a  super-tonic 
cfiord.  This  may  be  reckoned  as  a  chromatic  chord,  for  the  nb, 
although  not  unmistakably  in  the  key,  has  a  very  strong  progres- 
sion to  the  characteristic  chords  Ic  and  Vr 


134. 


88 


HARMONY  SIMPLIFIED. 


There  is  one  class  of  progressions  that  seem  to  lie  between 
transitions  on  the  one  hand  and  chromatic  chords  on  the  other. 

Any  chord  of  the  key  (except  the  Vll°)  may  be  preceded  by 
a  major  chord  (with  or  without  a  minor  seventh)  formed  on  the 
fifth  above,  and  still  no  real  transition  be  produced.  Thus  the 
progression  III,  VI,  if  followed  immediately  by  the  proper  pro- 
gression of  the  vi,  will  give  very  little  effect  of  transition.  Such 
progressions  are  the  same  as  passing  transitions,  only  they  are  so 
very  fleeting  that  the  result  is  simply  a  strengthening  of  the 
original  chord  by  giving  it  a  quasi  tonic  effect.  Notice  that  the 
progression  is  in  each  case  the  same  as  V  or  Y7  to  I  or  I.  Figure 
135,  a,  gives  a  series  of  such  progressions.  Figure  135,  i,  shows 
a  somewhat  similar  progression,  each  chord  having  a  seventh 
added ;  in  this  case  no  sooner  is  a  key  indicated  by  a  V7  than  it 
is  contradicted  by  another  V7,  giving  such  a  shifting  of  harmonies 
and  key  relationships  as  may  well  be  called  kaleidoscopic.  The 
sixth  chord  is  the  n7  in  the  key  of  C  and  progresses  regularly, 
but  the  fifth  chord  progresses  to  it  in  a  very  irregular  way. 

a.  BEETHOVEN.     Op.  14,  No.  2. 


135. 


/L" 

| 

i     n 

EH 

1             i 

L      i 

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S3* 

U.                             _l 

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J     J     j 

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0"^" 

<?••  VM 

-U 
I 

CHOPIN.     "Mazurka,"  op.  17,  No.  1. 


-^~  TTTF-  < ^ 

?CZI    ~    j       [    [•      ghflf         hL 


^^ap 


t!*==* 


HARMONY    SIMPLIFIED. 

Exercise. 

First.  —  Harmonize  the  following  soprano. 
136.  EX z 


89 


1 


VT  TT  TT  V 

iwl  7b  7d 


III  VI 

Second.  —  Complete  and  write  the  numerals  to  the  following. 

t_4_J_rL  _  i  •  fl         J     rt 


137. 


I 


^ 


i 


v+ 


fc=S 


JEE^E  Eg^fe 


li 


^^ 


i 


IIK   III     II    II, 


7,13 


90 


HARMONY  SIMPLIFIED. 


CHAPTER   XXII. 
Mixed  Chords. 

Mixed  chords  are  so  called  because  they  contain  an  inter- 
val —  the  augmented  sixth  —  which  cannot  be  formed  in  the 
scale  of  one  key,  but  requires  the  mixing  of  two  scales.  There 
are  three  of  these  chords,  all  containing  this  interval.  Figure 
138,  a,  b,  c.  They  are  generally  called  the  chords  of  the  aug- 
mented sixth,  the  first,  Figure  138,  a,  being  the  so-called 
French,  the  second  (5)  the  so-called  Italian,  and  the  third  (<?) 
the  German  sixth.  The  lettering  for  these  chords  is  somewhat 
complicated  and  is  as  shown  in  the  figure.  These  chords  origi- 
nate in  the  minor  mode  where  the  n  is  by  nature  a  diminished 
chord,  and  the  iv  a  minor  chord.  By  combining  with  these  two 
chords  the  characteristic  tone  of  the  dominant  key  (Fe)  the 
chords  are  produced  as  shown.  The  interval  of  the  augmented 
sixth  almost  invariably  appears  in  the  outer  voices,  though  the 
chords  may  be  used  in  other  positions.  They  progress  normally, 
to  the  Ic,  V,  or  Vr 


138. 


HARMONY  SIMPLIFIED.  91 

Figure  138,  g,  shows  the  growth  of  these  three  chords. 


French.  Italian.  German. 


As  the  vir°  of  the  major  mode  is  the  n°  of  the  relative  minor 
mode,  similar  chords  may  be  based  on  the  vu°  (11°  of  the  minor 
mode)  or  on  the  Jii°  (*iv°  of  the  minor  mode).  Figure  138,  d. 
It  is  best  to  regard  these  as  belonging  to  the  minor  mode  and 
borrowed  for  use  in  the  major  mode  rather  than  as  chords  formed 
in  the  major  mode.  They  are  really  examples  of  passing  tran- 
sitions. In  the  same  way  the  same  chord  is  found  apparently 
based  on  the  dominant,  but  it  is  no  more  a  part  of  the  key  than 
any  other  chromatic  or  transitional  chord.  Figure  138,  e.  It 
would,  however,  be  possible  to  regard  this  last  as  an  altered  chord, 
that  is,  a  V7,  with  the  fifth  flattened.  A  great  deal  of  confusion 
exists  among  writers  on  harmony  regarding  these  chords,  but  the 
student  may  avoid  it  all  by  remembering  that  there  are  but 
three  such  chords  possible,  the  three  shown  in  Figure 

138,  a,  b,  c.      All  others   are   borrowed  from  other  keys  and 
should  be  so  regarded.     Some  composers,  however,  not  liking  to 
see  the  E  flat  (for  example)  in  the  first  chord,  Figure  138,  c, 
progress  upward,  have  written  it  as  Dft.     This  notation  should 
be   avoided,  as  the  chord  is  the  same  whether  the  E{?  remains 
stationary  into  the  I  or  progresses  upward  to  E  natural  of  the  I. 
On  account  of  the  similarity  of  the  augmented  sixth   and    the 
minor  seventh,  both  intervals  being  represented  by  the  same  keys 
on  a  keyed  instrument,  they  are  sometimes  used  interchangably. 
Thus  if  the  German  chord  of  the  augmented  sixth  in  the  key  of 
C  be  written  as  at  Figure  138,  /,  instead  of  as  at  Figure  138,  c, 
we  have  the  V7  of  D  flat,  at  once  changing  the  key.     This  change 
of  Ftt  to  G|?  is  called  an  enharmonic  change.     Such  changes 
are  made  to  effect  quickly  a  transition  to  a  remote  key.     Figure 

139,  a. 


92 


HARMONY  SIMPLIFIED. 


139. 


jO.- 


I 


e,      6J7,         db- 


V7    I 


flr:   »IV«K       I, 

By  the  use  of  the  same  expedient  the  chord  of  the  diminished 
seventh  may  be  written  in  four  ways,  and  hence  treated  as  belong- 
ing in  any  one  of  four  keys.  This  opens  up  almost  endless  possi- 
bilities of  transition  and  modulation.  Figure  139,  b.  These 
chords  although  played  the  same  on  the  piano,  are  in  the  keys 
of  G,  E,  BJ7,  and  DJ7.  Viewed  from  the  standpoint  of  the  key- 
board there  are  but  three  different  diminished  seventh  chords, 
although  they  may  be  written  in  twelve  different  ways.  Figure 
c. 


Exercise. 

First.  —  Write  out  the  three  chords  of  the  augmented  sixth 
in  six  different  keys. 

Second. —Write  out  the  twelve  diminished  seventh  chords 
(one  for  each  key),  noticing  how  they  coincide  on  the  keyboard. 

Third.  —  Harmonize  the  following  soprano. 


14O. 


Fourth.  — Write  a  sixteen-measure  exercise  consisting  of 
four  four-measure  phrases,  introducing  an  altered  chord,  a  chro- 
matic chord,  a  transitional  cadence,  and  a  mixed  chord.  One 
four-measure  phrase  may  be  written  in  the  relative  minor. 


HARMONY  SIMPLIFIED. 


93 


The  following  illustrates  the  use  of  some  of  these  chords. 

a.  SPOHR.     "Jessonda." 



— d i*H ah: — 


141. 


I  v 

[J_    J ± 


+ 


*gq  11     '  H- 

-fa— F- 


Fft=S=^ 


6:  V 


V?a         Ib 


•v-  -[-- 


a,v° 


b 


V7 


SCHUBERT.     "Minuet,"  op.  78. 


d==i=i=£=i=R^4 


'^, 


^ 


i 


rsrit    Q        r i       ~r™MT^M7M™T    I  T  tufeia m I     I      Fl 

^^^f^^_n^^=^^=^^ 


4.    -4.  4.  -I. 


no 


J.  FIELD.     "Nocturne,"  No.  18. 


-X-K&  1—             —  i  

\i  sS  

—f  —  *  —  1 

©>  4     J          • 

•^                     «*• 

^_ 

"               1      i 
-s-                  | 

: 

C^\  *      L7          S                   fl                  tf 

njljp          v 

J*?/          i                                            i 

531 

-^    U   /i                                                       1 

•^                   •** 

s 

i       •     ,         J 

U              ' 

.F:  I                              IT 

a. 

(1 

«IV 

.7) 
% 

V 

El 


94 


HARMONY  SIMPLIFIED. 


,  CHAPTER   XXIII. 
The  Flat  Sub-Mediant  and  Flat  Super-Tonic. 

There  are  two  chords  that  are  of  rather  frequent  occurrence, 
neither  of  them  strictly  new  chords,  but  chords  that  are  used  in  a 
new  way.  The  first  is  the  flatted  VI  used  chromatically  pro- 
gressing to  the  Ic  or  V?.  This  chord  belongs  to  the  minor  mode, 
but  is  also  used  in  the  major  mode.  Figure  142,  a.  See  also 
Figure  124,  c,  where  the  chord  on  D|?  is  really  a  bridge  chord,  be- 
ing first  the  flat  VI  and  then  the  I. 

The  other  chord  is  formed  on  the  flatted  super-tonic  tone 
and  is  sometimes  called  the  chord  of  the  Neapolitan  sixth.  It 
is  used  in  either  the  major  or  the  minor  mode,  generally  in  the  b 
position  and  progressing  as  a  n  to  the  Ic  or  to  the  Vr  Figure 
142,  b,  and  Figure  143.  See  also  Figure  158,  second  measure. 


142. 


I>VI      I 


143. 


BEETHOVEN.     "  Funeral  March,"  op.  26. 

*  "  *'• 


at>;  I 


HARMONY  SIMPLIFIED.  95 

We  have  now  studied  all  the  chords  used  in  musical  composi- 
tion. In  the  following  chapters  we  shall  study  the  use  that  is 
made  of  non-harmonic  tones.  The  student  in  reading  musical 
compositions  will  no  doubt  find  chords  progressing  differently 
from  the  progressions  given  in  these  chapters.  This  is  especially 
true  of  the  compositions  of  the  most  modern  writers.  Such  pro- 
gressions need  cause  no  surprise.  They  hold  the  same  position 
in  music  that  the  liberties  taken  by  poets  hold  in  language.  As 
in  poetry  the  ordinary  rules  of  grammar  are  usually  observed,  so 
in  musical  composition  the  rules  of  musical  grammar  as  given  in 
these  pages  are  usually  observed.  It  is  only  for  special  effect 
that  they  may  be  violated.  Taste  and  *  experience  alone  will  de- 
termine whether  the  effect  is  a  good  or  a  bad  one.  It  will  be 
found  that  in  all  good  progressions,  no  matter  how  abrupt  or  ir- 
regular they  may  seem,  there  is  always  some  connection  between 
the  chords,  or  some  aesthetic  idea  that  is  of  sufficient  importance 
to  override  the  natural  progression  of  the  chord.  For  instance, 
the  V7  of  the  key  of  C  may  go  directly  to  the  Ic  of  the  key  of  B, 
apparently  a  most  irregular  progression.  But  if  instead  of  the 
seventh  F  in  the  first  chord  we  write  the  augmented  sixth  E& 
our  chord  becomes  the  German  sixth  of  the  key  of  B  and  pro- 
gresses regularly.  Figure  144. 


144. 


Other  irregular  progressions  are  explained  as  being  delayed 
progressions,  of  which  we  have  had  some  examples.  Others  again, 
are  produced  by  substituting  a  similar  chord  for  the  one  ex- 
pected. Still  others  come  by  the  progression  of  the  individual 
voices  which  for  the  moment  may  be  of  more  importance  than  the 
harmonic  progression. 


96 


HARMONY  SIMPLIFIED. 


If  chords  always  followed  their  bent,  that  is,  always 
progressed  normally,  we  should  be  constantly  having  ca- 
dences ;  music  could  possess  no  variety,  and  the  expres- 
sion of  moods,  feelings,  and  experiences  would  be  impos- 
sible. But  with  young  writers  the  tendency  is  usually  to  strive 
after  startling  changes,  "  pretty  effects,"  and  far-fetched  harmoni- 
zations. The  student  should  try  to  secure  first  a  smooth  easily- 
flowing  style,  and  then  if  his  taste  is  for  novelties,  he  will  run 
less  risk  of  introducing  them  in  such  a  way  as  to  make  himself 
ridiculous. 


Exercise. 

First.— Fill  in  the  parts  that  are  wanting  in  Figure  145  and 
write  the  numerals  underneath. 


145. 


* 


Second.— Write  two  sixteen-measure,  four-phrase  composi- 
tions introducing  the  i?II  and  the  ?VT  and  also  making  some  use 
of  altered,  mixed,  and  transitional  chords  when  they  can  be  em- 
ployed naturally.  Write  in  some  key  containing  more  than  two 
sharps  or  flats  and  in  four-four  or  six-eight  time. 


HARMONY  SIMPLIFIED. 


97 


CHAPTER   XXIV. 
Passing  and  Changing  Tones.     Appoggiaturas. 

Not  every  combination  of  tones  used  in  musical  com- 
position is  a  chord.  We  will  now  examine  the  different  ways 
of  using  tones  that  are  foreign  to  the  harmony. 

The  most  important  condition  in  using  non-harmonic  tones  is 
that  they  move  by  degrees. 

First.  —  When  a  tone  of  a  chord  proceeds  during  the  continu- 
ance of  the  chord  to  the  next  degree  above  or  below,  the  non- 
harmonic  tone  thus  introduced  is  called  a  passing  tone.  Figure 
146,  a. 

Rule  15.—  A  passing  tone  must  be  approached  and  left  by  de- 
grees. 

Second.  —  If  a  tone  fulfills  all  the  other  conditions  of  a  passing 
tone,  but  returns  at  once  to  the  tone  from  which  it  came,  it  is  a 
changing  tone.  Figure  146,  b.  Passing  or  changing  tones 
may  appear  in  two  or  even  in  three  voices  at  once.  Figure  146,  c. 

Third.  —  When  a  non-harmonic  tone  appears  at  the  same  time 
with  a  chord  tone,  proceeding  during  the  continuance  of  the  chord 
to  a  chord  tone,  such  foreign  tone  is  called  an  appoggiatura. 
Figure  146,  d.  Such  tones  may  be  approached  by  a  skip,  but 
they  must  be  left  by  degrees. 


d.+ 


146. 


9* 


F-- 

=£ 


J-J-, 


_ 

-jg- ^=|-ig a \J 

=p r— l-r^=n^=^ 


ii 


98 


HARMONY  SIMPLIFIED. 


Figure  147,  a,  the  fifth  note  in  the  soprano  is  a  changing  tone 
Figure  147,  6,  the  third  note  in  the  soprano  is  an  appoggiatura, 
and  the  fifth  is  also  a  changing  tone.  Figure  147,  <?,  the  notes 
marked  with  a  cross  are  passing  tones. 


BEETHOVEN.     "  Mondo  in  C. 

-,      b.  ' 


147. 


2* 


•II 


:qz=q=diE 
-•—     — •+* 


cM 


— 1 — ^ 

+  KUHLAU.     Op.  55,  No.  3. 


Exercise. 

First. — Harmonize  Figure  148,  treating  some  of  the  tones  as 
non-harmonic  tones. 


148. 


tt3^=^&&^^L 

[-%=£=*— 


Second.— Take  any  three  of  the  exercises  previously  written, 
and  rewrite  them  introducing  non-harmonic  tones  wherever 
they  can  be  effectively  used.  Do  not  try  to  use  as  many  as  possi- 
ble, but  rather  to  use  them  as  well  as  possible. 


HARMONY  SIMPLIFIED. 
Third.- -Complete  Figure  149. 


99 


149. 


ur 


i=-=^i 

r=g±?=i,-F-^»-F-J 


>..  V  A.   j 


U 


1 


;5^E-:^: 


aW-r*-, 


0 


93 


^ 


:«i|--         _f=5 

^c/-^j 


H 


100 


HARMONY  SIMPLIFIED. 


CHAPTER   XXV. 
Anticipation.    Pedal  Point. 

Fourth. — When  a  tone  belonging  to  one  chord  is  introduced 
as  a  non-harmonic  tone  into  the  preceding  chord,  it  is  called  an 
anticipation  or  an  anticipatory  tone.  Figure  150.  This  oc- 
curs frequently  at  the  end  of  a  period  or  of  a  whole  composition. 
Many  of  Handel's  pieces  end  thus.  See  also  Figure  112. 


BEETHOVEN.     Op.  49,  No.  2. 


150. 


yr  "  a 

i                                                                          1 

ffn      i          m 

J                                         _i         •       s-j             1 

HZ    4-         • 

•      1      &            -                                         j  .           9            &                      || 

f-    -r   f-        -^   -t   A     «    f- 

^v  •  IP   o                   • 

F            ~             F                     II 

1  •  Jff  P  J                  | 

J-         -                i-           0           i  E  -TzsJ  IH 

±  —  4  * 

^     -       |-     t  —  ,      ,      -      *-*^     H 

HANDEL.     "  Angels  ever  Bright." 

X  u  »i  *  —  r*  —    —  N  —  r  —  ~f*2~  ~1  —  H 

//r\P    *±       D       ^   ^     *       • 

IS^IJ         I/       "                          T  •  *     *       |"| 

O    take    me        to       your  care. 

/ 

XL  h  1    ^       ^^ 

1 

ifh9                               i 

| 

VMJ          «       g,       4         "If          -™       " 

'*'   T     :S:   :J 

1 

a-    r  *i  J    -«—  i       .. 

f 

1 

^  ^  ^  ^          ^  •! 

Fifth. — By  an  extension  of  such  passages  as  the  one  shown  at 
Figure  146,  c,  the  bass  tone  may  be  held  indefinitely  and  quite 


HARMONY  SIMPLIFIED. 


101 


independently  of  the  harmonies  of  the  upper  voices.  Such  use 
is  called  pedal  point.  It  no  doubt  originated  in  organ  playing, 
where  a  tone  is  frequently  held  with  the  foot  on  the  pedal  board, 
while  the  hands  play  the  manuals  quite  independently.  The  in- 
dependent tone  usually  occurs  in  the  bass,  but  is  sometimes  found 
in  any  one  of  the  other  parts.  Generally  it  is  the  dominant  or  tonic 
tone  that  is  so  held.  It  is  immaterial  whether  the  pedal  point 
be  held  throughout  or  constantly  repeated,  see  Figure  151,  a,  and 
151,  b. 

Rule  16.— The  beginning  and  the  end  of  the  pedal  point  must 
be  a  part  of  the  harmony.  Figure  151,  b. 

It  would  require  too  much  space  to  quote  many  illustrations 
of  pedal  point,  but  the  student  may  refer  to  any  or  all  of  the  fol- 
lowing: Heller,  "Slumber  Song  "from  op.  81,  the  repeated  A{?  ; 
Chopin,  "  Berceuse,"  in  which  the  low  DJ?  of  the  bass  held  by  the 
damper  pedal  occurs  in  every  measure,  and  the  harmony  scarcely 
varies  from  I,  V7 ;  Chopin  prelude  in  Di?,  the  Aj?  or  G|ft  is  heard 
nearly  all  the  time.  In  Wagner's  "Siegfried"  there  is  a  passage 
in  which  the  horns  hold  a  tone  through  some  thirty-four  measures 
—  an  extreme  example  of  a  pedal  point  in  a  middle  voice. 

The  following  illustrates  the  use  of  the  pedal  point  both  in 
sustained  form  and  in  repeated  form.  See  also  Figure  158. 


151. 


BACH.     "Prelude,  No.  22." 


*+  n  H^  H    H-^  j^  n^  /j 

PT          •*-    i*  *••-         H»- 

^-          D    I  *  \  \j 


^^ff-rrj^g 


Pedal  Point. 


102 


HARMONY  SIMPLIFIED. 

GADE.     "  The  Crusaders. " 


'I  s  'I  .0. 


Pedal  Point. 


Exercise. 


Harmonize  the  following. 


152. 


UK  IV 


-I L 


II7V7vi 


153. 


I  I  I 


-<& 0 •- 


^ 


=i 


7c 


:fc=^ 


J=M=>ti 


I 


Ic      g: 


HARMONY  SIMPLIFIED. 


103 


/Lb 

Ifh            «                mm 

__  2 

J 

•         1 

cJ 

Ri-fr  —  ^—    —  *  f  

=e  

9 



2.  b 

.. 

0 

s 

r 

1  ITO      n?d       i  VI       i,ob        ,o  V7>13  V7       I 


104  HARMONY  SIMPLIFIED. 

CHAPTER   XXVI. 
Suspensions   or  Retardations. 

Sixth.  —  By  far  the  most  important  method  of  using  non- 
harmonic  tones  is  as  follows.  When  a  tone  of  a  chord  is 
delayed  and  is  heard  in  the  following  chord  as  a  dissonance,  it  is 
called  a  suspension  or  retardation.  Figure  154,  a  and  b. 
The  tone  is  first  heard  as  a  consonance,  and  becomes  a  non-har- 
monic tone  by  being  held  while  the  rest  of  the  chord  changes. 
The  dissonant  tone  must  come  to  consonance  during  the  second 
chord.  The  suspended  (non-harmonic)  tone  usually  moves  down 
one  degree  in  resolving,  but  Te  may  be  suspended  before  Doh. 
If  the  delayed  tone  does  not  become  a  dissonance  in  the  second 
chord,  but  simply  forms  a  new  chord,  it  is  not  regarded  as  a  sus- 
pension. Figure  154,  d.  A  suspension  differs  from  a  dissonant 
chord  in  that  the  suspended  tone  is  first  heard  as  a  con- 
sonance, and  then  resolves  during  the  continuation  of  the 
next  chord;  while  the  dissonance  resolves  with  the  chord. 
Compare  Figure  154,  b,  and  154,  c.  In  other  words  the  sus- 
pended tone  is  foreign  to  the  chord ;  the  dissonant  tone  is  a 
part  of  the  chord. 

The  suspension  usually  occurs  on  the  accented  part  of  the 
heat  or  measure.  The  tone  to  which  the  suspended  tone  goes 
should  not  be  heard  with  the  suspended  tone  at  a  less  distance 
than  an  octave  below.  Figure  154,  e.  In  four-part  writing  it 
is  best  that  the  tone  to  which  the  suspended  tone  goes  should 
not  be  heard  with  the  suspended  tone  at  all,  though  examples  of 
such  use  sometimes  occur. 

The  student  will  find  that  passing  tones,  appoggiaturas,  and 
suspended  tones  do  not  always  go  directly  to  the  next  degree  of 
the  scale,  but  move  first  to  the  tone  one  degree  above  or  below, 
or  even  skip  to  some  other  tone  of  the  chord.  Figure,  154,  /,  #, 


HARMONY  SIMPLIFIED. 


105 


A.  Such  progressions  are  to  be  classed  as  irregular,  and  had  best 
be  avoided  until  the  student  is  thoroughly  acquainted  with  the 
more  ordinary  methods  of  progression. 


154. 


/L 

1 

•      i 

r    1  1 

§rr\         ^- 

1    4 

1 

1                  I  L 

S3                                    1    • 

<^>             • 

»       1  • 

J 

•s. 

• 

0                                       "f 

T-        -I 

-           i 

*         f         f 

C\" 

-    1 

•         Pi 

I 

rj. 

p 

Z          r2 

:|  ^ 

"ri» 

1 

IV, 


+  Bad. 


Exercise. 

First  and  Second.  —  Complete  Figures  155  and  156.    The  sus- 
pensions are  marked  with  a  cross. 


155. 


/ 


a 


106 


HARMONY  SIMPLIFIED. 


/^H0 

—  g^- 

j          J       m       *          J 

V37  

L,i  —  i  —  «- 

-*  —  •  *— 

r~r+             '~v  r  i 

RT;  —  •  p  p  »- 

-1  

N 

III 


156. 


/L'»J      * 

•       •       J 

J 

•          «'    -•  — 

•       • 

3  J_ 

^-^^  5*  ' 

V,                XV 

V7,9 

V7 

c~\  *  o 

1  •    f  J              ^ 

==1—4  — 

1      ^^ 

i—  ^  

-\ 

Pedal  Point. 


^h— 

=s    * 

e  —  .     ^_ 

•    m  0    • 

z 

\9r  —         —  *  — 

H 

0 
IV       II7                   V7             vi 

F  1 

F—  fl 

Third.  —  "Write  the  descending  and  ascending  scale  of  B  in 
the  soprano,  using  any  length  of  notes  desired,  then  harmonize. 
Similarly  write  the  ascending  and  descending  scale  of  At?  in  the 
bass  and  harmonize.  Be  especially  careful  of  the  descending 
Te.  The  following  from  "Lohengrin"  is  a  beautiful  example  of  a 
harmonization  of  the  descending  scale.  The  student  is  now 
familiar  with  all  the  progressions  used. 


HARMONY  SIMPLIFIED.  107 

WAGNER.     Prelude  to  "  Lohengrin." 


8va. 


157. 


*m 


J— j- 


i 


m 


m 


/It-' 


vib 


^=^= H 

3E ! 13 


7c 


"b    lv7"b     Y7 

The  following  shows    pedal  point,  altered    chords,  |?II,  and 
suspensions. 


ROSSINI.     "  Stabat  Mater." 


158. 


Pedal  Point. 

g:  I      i  II     I'll        Ic      i  Sus.V 


BACH.     "Organ  Prelude." 


We  have  now  reached  the  limit  of  our  subject.  The  student 
it  is  hoped,  has  acquired  a  fair  knowledge  of  all  the  material  used 
in  musical  composition,  and  of  the  ordinary  methods  of  using  this 


108  HARMONY  SIMPLIFIED. 

material.  As  this  little  work  only  aims  to  give  the  barest  out- 
line of  harmony,  the  student  is  urged  to  enter  upon  the  study  of 
some  of  the  larger  works  which  deal  with  the  subject  exhaust- 
ively. If  these  few  chapters  have  influenced  any  to  make  a 
thorough  study  of  composition,  or  if  by  their  means  any  have 
gained  a  clearer  insight  into  the  contents  of  musical  compo- 
sitions and  the  material  used  by  all  composers  from  the  least  to 
the  greatest,  their  purpose  has  been  fully  attained. 


HARMONY  SIMPLIFIED  109, 


CHAPTER    XXVII. 

Figured  or  Thorough  Bass. 

Harmony  was  the  gradual  outgrowth  of  Counterpoint.  In 
the  latter  it  was  the  intervals  between  the  voices  rather  than  har- 
monic progressions  that  were  regarded  as  of  the  highest  impor- 
tance. Thus  it  was  formerly  the  custom  to  regard  each  voice 
as  simply  a  certain  interval  above  the  Bass,  not  as  a  component 
part  of  a  chord.  With  this  in  mind  it  was  customary  to  write  a 
Bass  part  only  and  place  figures  under  each  note  indicating  what 
intervals  were  to  be  taken  by  the  upper  voices.  Thus  a  G  in  the 
Bass  with  the  figures  5  (  read  down,  seven,  five,  three  )  under  it 
would  indicate  that  the  upper  voices  sang  the  3d,  5th  and  7th 
above  G —  or  as  we  say  now  V7  (  key  of  C  ) .  It  is  to  be  noticed 
that  so  long  as  these  intervals  appear  in  the  upper  voices,  it  is  a 
matter  of  indifference  in  what  order  the  voices  take  these  inter- 
vals—  the  7th  for  example  may  be  in  any  one  of  the  upper 
voices.  Modern  Harmony  pays  comparatively  little  attention  to 
intervals  and  their  arrangement,  concerning  itself  rather  with 
melodies  and  their  harmonization,  harmonic  progression,  sonority 
of  effect,  etc.  Thus  while  the  modern  composer  looks  at  his 
composition  largely  as  a  series  of  chords,  each  of  which  has  its 
own  character — almost  its  own  individuality — the  older  writers 
regarded  their  compositions  as  a  number  of  layers  ( voices ) 
arranged  at  certain  intervals  above  the  Bass.  Although  the 
figured  Bass  spoken  of  above  is  gradually  falling  into  disuse,  still 
the  student  is  certain  to  find  it  in  his  reading  and  it  will  be  well 
for  him  to  have  some  knowledge  of  it  —  especially  as  the  princi- 
ples on  which  it  is  based  are  very  simple.  They  are  as  follows : 

Any  figure  underneath  a  Bass  note  requires  the  writing  of 
the  corresponding  interval  above  the  Bass.     Thus, 


110 


UARMONY  SIMPLIFIED. 


3       1 


1 


is  the  same  as 


The  number  of  notes  written  is  of  no  importance  provided 
we  write  at  least  one  for  each  figure.  In  other  words,  the 
figuring  is  the  same  for  any  number  of  voices,  three,  four,  five, 
six  or  more.  The  order  in  which  the  intervals  appear  above 
the  Bass  note  is  immaterial.  Thus  Fcjj— -  :  may  be  written  in 
any  of  the  following  ways 


Bj=E 


I/ 

M  J        £)          ^^TJ 

U 

etc. 
/•?          I 

t\*        ^ 

~                  II 

II 

The  figures  always  refer  to  the  intervals  as  they  stand  in  the 
signature.     Thus  pt^-fr—  ~^p=H  requires    the    minor 

7th  to  be  written  E=£^zi^i==i33  over  the  Bfr,  the  C 

7777 

and  the  D,  but  the  major  7th  over  the  EJ7. 

In  order  to  simplify  the  writing  of  figures  it  is  customary  to 
omit  certain  ones.  Thus,  when  no  figure  at  all  is  written  it  is 
understood  that  the  intervals  I  are  required,  i.  e.,  the  written  note 
is  the  Bass  of  a  common  chord  in  A  position  (unin verted).  In 
the  form  3  the  figure  3  is  usually  omitted.  The  figure  8  is  al- 
ways omitted  unless  such  omission  might  cause  misunderstanding. 


HARMONY  SIMPLIFIED. 


Ill 


yr 

& 

Ill 

(rK                    L  & 

0 

«       ^j 

saz                 i  5:      i 

*         1 

&       o 

or              means              or             means                  implies       but 

C~"\  . 

.                         \ 

II  i 

i  • 

\      (S           & 

-S           /p               S3 

,0     .. 

a. 

II 

If  it  is  necessary  to  affect  any  interval  by  an  accidental,  the 
proper  symbol  7,  jj,  ft,  etc.,  is  placed  before  the  figure,  but  an  acci- 
dental alone  always  refers  to  the  third  above  the  Bass.  Thus  : 


If  the  Bass  part  moves  by  a  passing  tone  the  other  voices  are 
to  remain  stationary ;  instead  of  writing  out  the  new  figures  to  cor- 
respond with  the  new  intervals  made  by  the  change  in  the  Bass, 
it  is  usual  to  write  horizontal  lines  in  the  place  of  figures,  Thus : 


L 


The    line  also  is  used    to  indicate    the    continuance    of   any 
figure,  as 


-f\                & 

1               "        II 

En 

,-r, 

g                                   II 

O 

f~X  "               >^ 

12                    || 

I  .              ^y 

-S 

II 

i  'i 


112 


HARMONY  SIMPLIFIED. 


Thus  the  student  will  notice  that  in  suspensions  the  left  hand 
figures  indicate  the  suspension,  the  right  hand  figures  the  resolu- 
tion, as, 

:J •      J^-J     ^ 


When  there  is  a  cnange  in  the  upper  voices  while  the  Bass 
note  is  held  the  figures  are  written  side  by  side.     Thus, 


m 


or  as  in  the  preceding  two  illustrations. 

It  was  formerly  customary  when  an  interval  was  to  be  raised 
a  semitone  to  indicate  it  by  a  stroke  through  the  figure,  /,  $,  etc. 
This  symbol  is  rarely  found  now  except  in  the  case  of  the  $ 
which  is  often  used.  $  means  of  course  the  same  as  jj6. 

In  order  that  the  student  may  become  familiar  with  the  fig- 
ures, he  is  advised  to  turn  back  in  his  exercise  book  and  write 
the  proper  figured  Bass  under  numbers  56,  83,  109,  121,  137. 
He  should  also  write  out  the  proper  notes  for  the  following  fig. 
ured  Basses  and  when  complete  add  the  numerals  indicating  the 
chords. 


HARMONY  SIMPLIFIED. 

•      | 


113 


— f—3 g-Tfcg — 


I* 


7  5 


I        7 


114 


HARMONY  SIMPLIFIED. 


^  APPENDIX   A. 

Below  are  given  illustrations  of  the  use  composers  make  of 
the  characteristic  effects  of  each  tone  of  the  scale. 

Doh.  Rest,  home.  Example  No.  1.  Also  the  ending  of  al- 
most any  composition. 

MENDELSSOHN.     "Elijah." 


1. 


And  when  he    had  said  this    he    ....    fell         a  -  sleep. 


Te.  Piercing,  pressing  upward.  No.  2,  the  cry  of  the  Sav- 
iour on  the  cross,  shows  very  dramatically  the  piercing  effect  of 
Te  dying  away  into  the  restful  Doh. 

GOUNOD.     ' '  Redemption. ' ' 


m 


:f: 


g_r 


g- 


& 


ii 


v  i 


My    Fa  -  ther,       In-  to  Thy    hands         I  corn-mend  my  Spir  -  it. 
No.  3  shows  the  upward  thrusting  effect  of  Te. 


STAINER.     "  Crucifixion. " 
+ 

•ft. 


I 


So         must    the       Son      of    Man         be       lift  -   ed      up. 

Lah.  Sorrowful.  Illustrated  in  No.  4.  Also  in  almost  any 
piece  written  in  a  minor  key,  where  Lah  is  the  root  of  the  minor 
tonic. 

STAINER.     "Crucifixion." 


I     am  lone        in  -  deed. 


HARMONY  SIMPLIFIED. 


115 


Soh.  Bold,  rousing.  Shown  in  Nos.  5,  6,  7,  8.  This  is 
very  common.  A  bugle  or  trumpet  call  almost  invariably  makes 
use  of  it. 


MENDELSSOHN.     "St.  Paul.' 


5. 


yr  "ii          | 

-, 

—  ;                       -3 

ESS 

•^  —  t  &         &     - 

zz        s  -^    .  -  ^ 

*./                  rZ) 

Sleep    -    ers,      wake,          a        voice          is         call    -     ing. 
MENDELSSOHN.     '  '  Elijah.  '  ' 

,,    u.               ",*"           ~f~      ~f~          m 

6.  : 

C\'K  H\L   Vr         \                i7 

_(  r_« 

'-J.Jfu+TJ*   tt         1                 L^ 

I        II 

Call     him  loud  -  er. 


VERDI.     ' '  Trovatore. ' ' 


7.  ^|§EEgggE^^^g^^^ 


A  -  rouse       ye,  a  -  rouse      ye  ! 


HAYDN. 


Creation.' 

+  ^ 


8. 


==t= 


The  Lord      is      great, 


and    great    His     might. 


Fah.  Solemn.  This  effect  is  well  shown  in  No.  9.  Another 
example  is  the  ordinary  use  of  this  tone  in  the  "  Amen  Close  "  of 
church  music. 

STAINER.     "Anthem." 

+ 


When     sin  -  ners  meet  their     aw  -  ful    doom. 


Me.  Quiet,  plaintive.  In  Nos.  10  and  11  the  peculiar  ef- 
fect of  Me  is  easily  heard.  No.  10  expresses  rest  as  no  other 
tone  could,  and  the  plaintiveness  of  No.  11  is  unmistakable. 


116 


HARMONY  SIMPLIFIED. 


MENDELSSOHN.     "Elijah." 

+ 


10. 


O    rest     in    the  Lord. 


HANDEL.     "  Angels  ever  Bright." 


Take,  0   take  me,    take  rne,    take  me. 


Ray.  Expectant.  The  character  of  Ray  is  the  least  impres- 
sive of  all,  but  if  the  student  will  try  the  two  examples,  Nos.  12 
and  13,  he  will  see  that  no  other  tone  could  be  used  as  well  —  es- 
pecially in  separating  the  verb  from  its  object  by  three  measures 
rest  as  in  No.  13.  Let  the  student  sing  No.  13,  using  Doh  in- 
stead of  Ray  for  the  word  "  bring  "  and  note  the  effect. 

HOFMANN.     "Melusina." 


A  -  rise, 


HANDEL.     "Samson.' 


Ye    men     of      Gaz     -    a,      hith   -   er  bring 


The 


HARMONY  SIMPLIFIED. 


117 


APPENDIX   B. 

The  following  exercises  are  given  that  the  teacher  may  have 
an  additional  number  of  exercises  from  which  to  draw  in  case  he 
wishes  to  increase  the  amount  of  work  done  by  the  pupil.  Some 
of  them  contain  exceptional  uses  of  the  chords,  many  of  these 
being  marked  with  a  cross.  The  student,  however,  should  not 
make  use  of  such  progressions  unless  they  are  especially  marked. 
It  is  hoped,  too,  that  an  added  interest  is  given  by  introducing 
several  well-known  melodies  and  short,  excerpts  from  standard 
composers.  The  latter  are  sometimes  slightly  altered  to  admit 
of  being  used  by  the  student  at  his  present  stage  of  development. 

The  teacher  is  of  course  at  liberty  to  add  exercises  of  his  own 
making,  or  those  taken  from  other  works  on  harmony,  as  he  may 
see  fit. 

In  lettering,  a  dash  after  a  letter,  as  V  — ,  indicates  that  the 
chord  is  sustained  another  beat  without  repetition.  A  bracket 
under  several  letters  indicates  that  they  come  within  the  time  of 
one  beat. 

Chapter  I. 


i  Ht2  i  v  I  v  i  I    ill  v—  I    ill    v  v  I    i  v  I  i— 

JL  •     I    ~7      fc-v 


\^A 


I] 


— e>      ^—-&—: 


IVIVIVI         IVIIVVI 


3. 


118 


HARMONY  SIMPLIFIED. 


4. 


x^fl         •   » 

•                   <—  ' 

w                               t 

m^  •  —      —  •— 

Rf-fr  — 

-_  1 

\  F  -•••  F  

.  r  _ 

Chapter  II. 


i 


F      F — F- 

r— r— r 


6. 


7. 


n        J       1                   •             i      1       !     J       ! 

u  s)   &>     a 

J 

J      « 

^x          -^- 

^/             /^" 

S:^ 

-^  — 

J 

-12  — 

<jy      ** 



WAGNER.     AIT. 


- — "- — -^-- 


Chapter   III. 

Mark  the  following  intervals  taken  from  Chopin's  "  Polonaise 
in  Cjk  minor." 


8. 


^ 

--  — 


9. 


f^~Y~  jLbJ^^y^-^-^g^  gUjJO j 

.fzJjfG.fc.^^  ^      -  ^  -*>- 


HARMONY  SIMPLIFIED.  119 

Write  above  the  following  the  intervals  marked. 

M.  3.    m.  3.    A.  4.     D.  5.     M.  5.     D.  7.    M.  6.   m.  6.    M.  2.    D.  3.     M.  3.    m.  6. 


Chapter  IV. 


3=  E=^= 


1 — i — u 1 =— "— (9 — fy  ' 


12. 


&*=*- 

i 

-h.      .  • 

0  

II  I.        V          I  V  VV 


0         !         J       J                                  I__L_1__J!LJ 

—x-  —  J      -*-  — 

1 

1 

*  *       ^ 

-=H- 

m 

—  *  —  ^— 

=i— 

—  H 

I  I         IV        IV    IV        I          I          I        T  V      V          I 


"Auld  Lang  Syne." 


13 


J-- 


120 


HARMONY  SIMPLIFIED. 

Chapter  V. 


BUSSLER. 


^ 


14. 


15. 


I 


v  _         '    <* 


16. 


r 


II 


^ 


f-f-T 


v  i/  tx- 


rK 


Jl 


Chapter  VI. 


IV 


7d 


V7b    I    I  Ie     V7 


rr 


V      V 

V7cX7b 


-^~ 


-> — ^- 


IV 


19. 


^ ,   i— n™^   —i   i  H  i  — « i**i  r*i "^ 


P'» 


*  *  ? 

LU 


HARMONY  SIMPLIFIED. 


121 


1 


Chapter  VIII. 


PROUT. 


20. 


r  r 


[| 


V7d         V7b         "t, 


I  IV     V     !       IV    IV     II  V  !        IV  V         I     IV       „       V 


„          b 


Tb  b        „        ? 


22. 


-UJ 


I 


7d 


EH: 


23. 


122 


HARMONY  SIMPLIFIED. 


TO  —            j 

—  J— 

LJ     r^?*i  —  i—  -*- 

[^  ^    t  U 

W 

4  .        W 

J  —  J  —  J  —  /_ 

x  • 

5^5  — 

,  •  — 

•      ...  *.. 

Chapter  IX. 


24. 


II 


Ib  vi    n   nb  Ic    V       I 


CHOPIN.     (Arr.) 


25. 


^t= 


m 


26 


j^=i=izz=i: 


MENDELSSOHN.     (Arr.) 


7c 


i      i    i    i 


7c  7d 


Ab  Ab    vb      V7b    V7  Lb 

Do  not  harmonize  the  appoggiaturas. 


HARMONY  SIMPLIFIED. 

Chapter  X<. 


123. 


27. 


ivb  vb  v7b 


B-H?— t ^=EEa 

3§Ei 


iv          i, 


fcrai£=PE 
-H — — i — H - — 

->-|__          1 


YI       IVb   V7b       IVC        Ib  IV 


28. 


Ht: 


I  I ^       L_  ^       r^^l 


V7b  V 


1=2: 


i 


V7       vi  ii  V        vi         IV 


29. 


izJ: 


V        m 


V     iiiv          vi       IV        V, 


V   vi   V, 


IV 


124 


HARMONY  SIMPLIFIED. 


Chapter  XI. 


•BO. 


iv 


V     V 


7d 


V7  vi    Ic  V?  I       Ib    IV  Ib         vi     vi       V 


?E3^ 


32. 


vug    Ib    mb  V7d  Ib   Ib    IVIVb      Ib       vi    vi     nb       V7        I 

BUSSLER. 


HUGOUNENC. 


33. 


•-).  /»           f 

S      \\J        (3 

r* 

^2 

^^ 

& 

•^ 

—            ^, 

/^ 

^2 

P' 

1 

r 

^~\ 

vii»          vug          vug 


ii      V      V 


b       ?b 


rrr  r'r  r'r-^r  r'rrn 


rc  I      IVC    I      vi      nb    V      mb  vi 


HARMONY  SIMPLIFIED. 

Chapter  XII. 


125 


34. 


-\- 


«=F^ 


M 


iiiS- 


BBE 


-•— 


:pzp; 


"7d 


I L/ — T7 1 

35.  gp§£Jfe^  =j=hiE        |=jgE^gEE?E 
^z-       p ..  I  » 


7b 


VI7b    »7d       V7b 


IV       ii 


I         V        in 


36. 


T= 


~f!-&- 


.   42.  jfi.  -&. 


37. 


ott 

i      1        h 

Folt 

.  Song. 

Vtri*  Q 

k.         1  m           J 

fc 

i           i  1 

l 

/L    »  O     i 

P  J            '        •       « 

__    __    J      , 

K 

q 

irh  Sta 

J     * 

J         J     J 

126 


HARMONY  SIMPLIFIED. 

Chapter  XIII. 


"       H       VV       IJI       V 


b        7        7,117          b         7 


39. 


-<s> •- 


II 


¥i 


I 


II 


TT 


iv^ 


V          V 
V7,13  V7 


40. 


r7cl7IV  V7b^7 


iv7v? 


Chapter  XIV. 


STAINER. 


41. 


V   vi 


-f         4-  BtJSSLER. 


42. 


:p=»: 


rv 


IV     ii 


HARMONY  SIMPLIFIED. 


127 


V      in     I       vi     IV     ii 
In  Nos.  43  and  44,  the  crosses  mark  the  by-tones. 


43. 


fe£ 


i 


i"T 


Chapter  XV. 


45. 12^8=13 


7d 


V      vi 


IVv 


46. 


-JV 


r 

Folk  Song. 


flr^K  J-  ^ 


V,.!,. 


128 


HARMONY  SIMPLIFIED. 


FINE. 


Double  Chant. 


47. 


J — J. 


d 


1 


Chapter  XVI. 


48. 


-i 1- 


fe 


rl 

* 


n.  i  _  i    i    i 

iT  J      J 

~^  —  • 


1 


Ivc         l     IvbV       V7d  rb     V7c 


FAIS^T. 


49. 


50. 


HARMONY  SIMPLIFIED. 

Chapter  XVII. 


129 


ZELTER. 

+  + 


liii 


A 


f---*- 


V       i 


VI        III 


IV  !„         II"         IV 


*— * 


I       ii       a;ic     VI    n°     V     i 


52. 


VI 


V7d      'b 


E3^E  3d 

^r        L —          -'      |  g ^ — ===Fg>        I  j 


VI 


*7b 


III+      VI          Ilg  Io 

™   1  »?bV7d    I   'b  VI   I   »?  V7b   |    i  iv  |  V  i   |   VI  „§   |   V7  i  || 


Chapter  XVIII. 


HANDEL.      (Arr.) 


•F— -*• 


11° 


+ 


55. 


BE 


D  :  ii,      V 


^ 


^ 


e 


7,9 


130 


HARMON!    SIMPLIFIED. 


m 


iv  VI 


V7,13"7c  V7 


56. 


±=M=i 


Chapter  XIX. 


STAINER. 


57 


7e 


• 


IV         V 


Hymn-Tune. 


58. 


-l.^t/i 

m—f-^—m 

•       F      •       r 

ZZ2  »  > 

I 

i    r  r 

P 

r^g 

*n   "      1 

- 

r   r 

Vb       vi  G:  I 

D:  ii        T      V     I 


?=*-£— E 


f=r 


-^-^ — •- 


ie  v7  ic  v7 


HARMONY  SIMPLIFIED. 


131 


$     r •     I  J     I I ; 


GUILMANT. 


60. 


'&. J 


^ 


;^I 


7c 


=4= 


J^-i 


=F± 


^ 


c:  V 


7b 


iv 


-.  v 


,d 


132 


HARMONY  SIMPLIFIED. 

Chapter  XX. 


61.E93 


V7,9        V7       I       »'b       V7       I 


IVc       »?d 


III       UK       II-H  11°.       V,,,       I       IK       IK       I       H-       V-,.       I     I  — 


^K —       — i-»-u<5| — L«- ' ' 


62. 


7b 


in 


J- 


"7b  V7d 


1 1+  iv  iv+  |  ii  n+  v—  |  in  ni7  vi  vi7d  I  nb  v7  i  — 


64. 


XL  b  h 

i          i 

i       -i       i 

i             i 

j 

PT  "2: 

ill 

ItZ3 

-_ 

fy 

2                k-L 

.c*      te1 

*^ 

cJ 

J                                         J       "" 

r 

C)f-t>  — 

1  —  s  — 

*^  — 

_, 

feHz—  * 

—  H1 

p 

5 



-^ 

is 

x^ 

^ 

1  K 

—  H 

B2  

2J 

L 

p\  *    h 

-p- 

3 

^=6-fr— 

—  p-  —  f 

± 

F 

—  t- 

HARMONY  SIMPLIFIED. 

Chapter  XXI. 

N.  B. 


133 


PROUT. 


'F- 


7b 


7d 


7b 


66. 


II7  V7  a :  i       V7b  i  C :  V 


IT  V7    Jc     'c   v     'c 


67. 


1 


1 


VIIT  i          vib7 


c    7c 


134 


HARMONY  SIMPLIFIED. 

Chapter  XXII. 


7,97 


«•'  Ivb*IV7b  'c  Td  V7,1ST7 
|  lb  F:   n  ii.,,  VK  I     |     L 


b  c 


69. 


gL     \_L\ r*L^-JU— fc- 


SE 


m 


^fe 


&=; 


D:IC 
±_ 


^_T 


25*-< 


G:  V, 


6:     i. 


I  'If 


II 


^ 


G:  V, 


7.13 


70. 


VI 


V      V?    VI      ivbjfiv^    V         a.'*iv<>    V 


HARMONY  SIMPLIFIED. 


135 


T  T      Ti         TV     tfrvO   V     V 

b         l     Jb7dlvb*lvb    v      V7 


*=f 

V    d: 


C:vnb°V7bI     Ib?  d:V 


VI      ivb   fiv°   V       V7  VI      ivb  fivg    V     iUvg    V    fivg    V 

-(2. 


VI     friio  IV 


i          V, 


r-T^TT— /»— *— /•-rS' »-r^— f— fi-f-e 


VI 


b       n7b 


Chapter  XXIII. 


^ J- 

te 


p 


— U-l. 


r^=^ 1— F 


— -— — -1 


— J—Tzt 


li 


-«>- 


1: 


3 
1 


136 


HARMONY    SIMPLIFIED. 


LISZT.     (Arr.) 


72. 


& 


I          vi          IV          I  ii  V7  9  V7 


7S355Z     i    '           *      • 

fm17  P  h                        •       * 

m 

_  _n 

i  

*^-l  -m 

1  

1  

vi        I7c    IV       I 


Ab :  ii       vn°          I  1+ 

ii       vi  Z>b :  V+    I        vi 


:  i       V      VI     iv 


£=i 


II 


I       Ik,  >VI 


-* — •- 

IV     ii        I 


73.E333  T  IV  V7,9  V7  I  IVb  V7bIVc   I  |  vib 


F:  I    I      I 


. 


i     Vi     iv 


c      7db 


b      c 


:n   n 


7d 


Chapter  XXIV. 


-J^*^ 


HARMONY  SIMPLIFIED. 


137 


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v  I     I    I    .  Irs-ll 


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76. 


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— a-i— r-i— 1~ 


PIP 


8 


i[:= 


3 


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1 


a.  a.      6.         a.  c. 

-PS- 


MENDELSSOHN. 
6. 


/ft-'"'          V7e 


S^E^E^gpfe^E^gg    r^Ff^H 
--=^-^±=1  ^^^-b^— ^Z=^+*^3=:^H-^J  I J     H 


a. — Passing  tones,     b.  —  Appoggiatura.     c.  —  Changing  tone. 


138 


78. 


HARMONY  SIMPLIFIED. 


Chapter  XXV. 


+ 


£-*=*: 


79. 


i 


Allegro. 


IV     ii 


'25 — 27 


J 


^^^j^^^JL^j^y^ 


>• 


—    —  -ft- 


^rb- 


m 


k  i 

jt 


bV 


HARMONY  SIMPLIFIED. 


139 


Exercise  80,  arranged  from  Chauvet,  illustrates  a  pedal  in  the 
upper  voice,  also  a  double  pedal.  Measures  9-14  are  to  be  writ- 
ten in  five  voices.  The  distance  between  soprano  and  alto  is  in 
several  places  greater  than  an  octave. 


80. 


J 


J 


JL 


/LS    i 

p 

A 

1 

« 

rTi^ 

• 

•          ^    1 

?     II 

V-y       1 

r_* 

11 

s 

L^F 

1          [^f 

f*^ 

U 

1 

r 

^-^  •      ^ 

1  •      [/ 

E 

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-*-n 

^7 

-o 

-X5  

-.-J 

si. 


C:  IV 


STAINER. 


:  V, 


82. 


140 


HARMONY  SIMPLIFIED. 


The  following  from  Bussler  shows  a  number  of  suspensions 
from  below.  In  the  last  chord  but  one  we  have  an  example  of 
the  suspension  of  three  tones  at  once.  This  might  also  be  called 
an  anticipatory  tone  in  the  bass. 


83. 


fet 


7c 


'7b 


IV 


/k  tt   •               • 

1  *  * 

i 

\>\J 

fc- 

*  —  *— 

^                                                           1  ~l     i 
xb                     v»b*              »b              |     , 

11                                                           -±-±  -*      • 

SZl 

/•#«• 

BACH.      (Arr. ) 


84. 


^pj 


Lm 


e 


E 


i 


n        -s  i 

iZ4  J       j^J     !        !-  !     1      fesJ           i- 

^^      t 

-    •       • 

m      m        d 

•      j         J 

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C        V 

lfl\        t?                      *^ 

\>l/                                   ' 

1 

b^rt>     [^            ^   [ 

-I2  ta~ 

-£t 

i 


dt^: 


-•       ^   1^ 


Repeat  the  bass  of  the  first  eight  measures. 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 

Los  Angeles  g  g  ^5 

This  book  is  DUE  on  the  last  date  stamped  below. 


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LIBRAi 

MT 
50 

Y63P7 
1909 


